Solutions / Properties of triangles for IIT-JEE MAINS /ADVANCED

Video lectures  of KAMAL SIR  for  Properties of triangles

 

 

QUICK   REVIEW

In a triangle ABC the angles are denoted by capital letters A, B and C and the length of the sides opposite to these angles are denoted by small letters a, b and c. Semi perimeter of the triangle is
given by s where  2s = a + b+c  and its area is denoted by Δ

SINE  RULE

Sine rule is an  important tool that relates   side lengths with angles of triangles  and circum radius of triangle

PROPERTIES OF TRIANGLE 1

NAPIER’S ANALOGY (TANGENT RULE)

PROPERTIES OF TRIANGLE

COSINE RULE
In a triangle ABC

properties of triangle -- cosine rule
properties of triangle — cosine rule

 

PROJECTION RULE

(i) a = b cos C + c cos B (ii) b = c cos A + a cos C (iii) c = a cos B + b cos C

HALF ANGLE FORMULAE

PROPERTIES OF TRIANGLE

 

.m-n THEOREM

PROPERTIES OF TRIANGLES

PROPERTIES OF TRIANGLES

 

CENTROID AND MEDIANS OF A TRIANGLE
The line joining any vertex of a triangle to the mid point of the opposite side of the triangle is called the median of the triangle. The three medians of a triangle are concurrent and the point of concurrency of the medians of any triangle is called the centroid of the triangle. The centroid divides the median
in the ratio 2 : 1.

 

Circum circle

PROPERTIES OF TRIANLES

The circle which passes through the angular points of a ABC, is called its circumcircle. The centre of this circle i.e., the point of concurrency of the perpendicular bisectors of the sides of the ABC, is called the circumcenter.

Radius of the circumcircle is given by the following formulae

PROPERTIES OF TRIANGLE
ORTHOCENTER AND PEDAL TRIANGLE OF A TRIANGLE.
In a triangle the altitudes drawn from the three vertices to the opposite sides are concurrent and the point of cuncurrency of the altitudes of the triangle is called the orthocenter of the triangle. The triangle formed by joining the feet of these perpendiculars is called the pedal triangle i.e.
DEF is the pedal triangle of ABC.

PROPERTIES OF TRIANGLES

 

BISECTORS OF THE ANGLES
If AD bisects the angle A and divide the base into portions x and y, we have, by Geometry,
properties of triangle

 

INCIRCLE
the circle which can be inscribed within the triangle so as to touch each of the sides of the triangle is called its incircle. The centre of this circle i.e., the point of concurrency of angle bisectors of the triangle is called the incentre of the ABC

properties of triangle

The distances Between the special points
properties of triangle

ESCRIBED CIRCLES
The circle which touches the side BC and the two sides AB and AC produced is called the escribed circle opposite the angle A. Its centre and radius will be denoted by I1 and r1 respectively.

properties of triangle

Excentral triangle
The triangle formed by joining the three excentres I1, I2 and I3 of
DABC is called the excentral or excentric triangle. Not that

properties of triangles

Inscribed & Circumscribed Polygons
(Important Formulae)

sot 46

 

SOLUTION OF TRIANGLES
When any three of the six elements (except all the three angles) of a triangle are given, the triangle is known completely. This process is called the solution of triangles.

sot 47

sot 48

 

Inverse-Trigonometric-Functions-objectives-with-solutions-Trigonometry-IIT JEE MATHS-Mains / Advanced

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse

P-Inverse Trigo Function-Objective-S-1-1
P-Inverse Trigo Function-Objective-S-1-1

SOLUTION

S-Inverse Trigo Function-Objective-S-1-1
S-Inverse Trigo Function-Objective-S-1-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and simple trigonometric calculations

P-Inverse Trigo Function-Objective-S-2-1
P-Inverse Trigo Function-Objective-S-2-1

SOLUTION

S-Inverse Trigo Function-Objective-S-2-1
S-Inverse Trigo Function-Objective-S-2-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and simple results involving inverse trigonometric calculations

P-Inverse Trigo Function-Objective-S-3-1
P-Inverse Trigo Function-Objective-S-3-1

SOLUTION

S-Inverse Trigo Function-Objective-S-3-1
S-Inverse Trigo Function-Objective-S-3-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and result of tan(A+B)

P-Inverse Trigo Function-Objective-S-4-1
P-Inverse Trigo Function-Objective-S-4-1

SOLUTION

S-Inverse Trigo Function-Objective-S-4-1
S-Inverse Trigo Function-Objective-S-4-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse

NOTE; Problem is not correct  pz see the solution for correct problem

P-Inverse Trigo Function-Objective-S-5-1
P-Inverse Trigo Function-Objective-S-5-1

SOLUTION

S-Inverse Trigo Function-Objective-S-5-1
S-Inverse Trigo Function-Objective-S-5-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and result of SIN(A+B)

P-Inverse Trigo Function-Objective-S-6-1
P-Inverse Trigo Function-Objective-S-6-1

SOLUTION

S-Inverse Trigo Function-Objective-S-6-1
S-Inverse Trigo Function-Objective-S-6-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and how we get the range of simple quadratic functions

P-Inverse Trigo Function-Objective-S-7-1
P-Inverse Trigo Function-Objective-S-7-1

SOLUTION

S-Inverse Trigo Function-Objective-S-7-1
S-Inverse Trigo Function-Objective-S-7-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their and domain and range of simple trigonometric functions

P-Inverse Trigo Function-Objective-S-8-1
P-Inverse Trigo Function-Objective-S-8-1

SOLUTION

S-Inverse Trigo Function-Objective-S-8-1
S-Inverse Trigo Function-Objective-S-8-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and graphs of defining of arcSIN(sinx) and arcCOS(cosx)

P-Inverse Trigo Function-Objective-S-9-1
P-Inverse Trigo Function-Objective-S-9-1

SOLUTION

S-Inverse Trigo Function-Objective-S-9-1
S-Inverse Trigo Function-Objective-S-9-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse

P-Inverse Trigo Function-Objective-S-10-1
P-Inverse Trigo Function-Objective-S-10-1

SOLUTION

S-Inverse Trigo Function-Objective-S-10-1
S-Inverse Trigo Function-Objective-S-10-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and defining of arcSIN(sinx) and solving simple quadratic inequalities

P-Inverse Trigo Function-Objective-S-11-1
P-Inverse Trigo Function-Objective-S-11-1

SOLUTION

S-Inverse Trigo Function-Objective-S-11-1
S-Inverse Trigo Function-Objective-S-11-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and domain and range of inverse of trigonometric functions, solving simple quadratic inequalities

P-Inverse Trigo Function-Objective-S-12-1
P-Inverse Trigo Function-Objective-S-12-1

SOLUTION

S-Inverse Trigo Function-Objective-S-12-1
S-Inverse Trigo Function-Objective-S-12-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and  simple results involving  inverse trigonometric functions ( arcTAN A -arcTAN B )

P-Inverse Trigo Function-Objective-S-13-1
P-Inverse Trigo Function-Objective-S-13-1

SOLUTION

S-Inverse Trigo Function-Objective-S-13-1
S-Inverse Trigo Function-Objective-S-13-1
S-Inverse Trigo Function-Objective-S-13-2
S-Inverse Trigo Function-Objective-S-13-2

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and domain and range of simple inverse trigonometric functions

P-Inverse Trigo Function-Objective-S-15-1
P-Inverse Trigo Function-Objective-S-15-1

SOLUTION

S-Inverse Trigo Function-Objective-S-15-1
S-Inverse Trigo Function-Objective-S-15-1

PROBLEM

 

P-Inverse Trigo Function-Objective-S-16-1
P-Inverse Trigo Function-Objective-S-16-1

SOLUTION

S-Inverse Trigo Function-Objective-S-16-1
S-Inverse Trigo Function-Objective-S-16-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and domain and range of inverse trigonometric functions

P-Inverse Trigo Function-Objective-S-17-1
P-Inverse Trigo Function-Objective-S-17-1

SOLUTION

S-Inverse Trigo Function-Objective-S-17-1
S-Inverse Trigo Function-Objective-S-17-1

PROBLEM

To understand this question of Inverse trigonometry you must know; The basic concept of sin ,cos ,tan , and their inverse , domain and range of simple inverse trigonometric functions , concepts of quadratic equations

P-Inverse Trigo Function-Objective-S-18-1
P-Inverse Trigo Function-Objective-S-18-1

SOLUTION

S-Inverse Trigo Function-Objective-S-18-1
S-Inverse Trigo Function-Objective-S-18-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse, domain and range and simple results

P-Inverse Trigo Function-Objective-S-19-1
P-Inverse Trigo Function-Objective-S-19-1

SOLUTION

S-Inverse Trigo Function-Objective-S-19-1
S-Inverse Trigo Function-Objective-S-19-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse , how  we change one inverse trigonometric function in 2   and result of ( arcTAN A -arcTAN B )

P-Inverse Trigo Function-Objective-S-20-1
P-Inverse Trigo Function-Objective-S-20-1

SOLUTION

S-Inverse Trigo Function-Objective-S-20-1
S-Inverse Trigo Function-Objective-S-20-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse defining and graphs

P-Inverse Trigo Function-Objective-S-21-1
P-Inverse Trigo Function-Objective-S-21-1

SOLUTION

S-Inverse Trigo Function-Objective-S-21-1
S-Inverse Trigo Function-Objective-S-21-1

PROBLEM

To understand this question of Inverse trigonometry  you must know;  The basic concept of sin ,cos ,tan , and their inverse and result of sin (A- B)

P-Inverse Trigo Function-Objective-S-22-1
P-Inverse Trigo Function-Objective-S-22-1

SOLUTION

S-Inverse Trigo Function-Objective-S-22-1
S-Inverse Trigo Function-Objective-S-22-1

 

Properties-of-Triangle-objectives-with-solutions-Trigonometry-IIT JEE MATHS-Mains / Advanced

To understand this question of properties of triangles you must know;  The concept  of sine rule 

PROBLEM

P-Properties of Triangle-Objective-S-13-1
P-Properties of Triangle-Objective-S-13-1

SOLUTION

S-Properties of Triangle-Objective-S-13-1
S-Properties of Triangle-Objective-S-13-1

PROBLEM

To understand this question  you must know;  The concept  of AM-HM inequality

P-Properties of Triangle-Objective-S-14-1
P-Properties of Triangle-Objective-S-14-1

SOLUTION

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, and conditions when two circles touch each other

P-Properties of Triangle-Objective-S-15-1
P-Properties of Triangle-Objective-S-15-1

SOLUTION

S-Properties of Triangle-Objective-S-15-1
S-Properties of Triangle-Objective-S-15-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of exradii, and conditions of AP,HP,GP

P-Properties of Triangle-Objective-S-16-1
P-Properties of Triangle-Objective-S-16-1
S-Properties of Triangle-Objective-S-16-1
S-Properties of Triangle-Objective-S-16-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule, basic concept of quadratic equation 

P-Properties of Triangle-Objective-S-17-1
P-Properties of Triangle-Objective-S-17-1

SOLUTION

S-Properties of Triangle-Objective-S-17-1
S-Properties of Triangle-Objective-S-17-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule, basic concept of quadratic equation 

P-Properties of Triangle-Objective-S-18-1
P-Properties of Triangle-Objective-S-18-1

SOLUTION

S-Properties of Triangle-Objective-S-18-1
S-Properties of Triangle-Objective-S-18-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of sine rule and triangle inequality

P-Properties of Triangle-Objective-S-19-1
P-Properties of Triangle-Objective-S-19-1

SOLUTION

S-Properties of Triangle-Objective-S-19-1
S-Properties of Triangle-Objective-S-19-1
S-Properties of Triangle-Objective-S-19-2
S-Properties of Triangle-Objective-S-19-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of orthocentre , cicumcircle and circumradius

P-Properties of Triangle-Objective-S-20-1
P-Properties of Triangle-Objective-S-20-1

SOLUTION

S-Properties of Triangle-Objective-S-20-1
S-Properties of Triangle-Objective-S-20-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule, sine rule and proving conditional trigo identities

P-Properties of Triangle-Objective-S-21-1
P-Properties of Triangle-Objective-S-21-1

SOLUTION

S-Properties of Triangle-Objective-S-21-1
S-Properties of Triangle-Objective-S-21-1
S-Properties of Triangle-Objective-S-21-2
S-Properties of Triangle-Objective-S-21-2
S-Properties of Triangle-Objective-S-21-3
S-Properties of Triangle-Objective-S-21-3

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule, sine rule and proving conditional trigo identities

P-Properties of Triangle-Objective-S-22-1
P-Properties of Triangle-Objective-S-22-1

SOLUTION

S-Properties of Triangle-Objective-S-22-1
S-Properties of Triangle-Objective-S-22-1
S-Properties of Triangle-Objective-S-22-2
S-Properties of Triangle-Objective-S-22-2
S-Properties of Triangle-Objective-S-22-3
S-Properties of Triangle-Objective-S-22-3

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of sine rule and ratio concept 

P-Properties of Triangle-Objective-S-23-1
P-Properties of Triangle-Objective-S-23-1

SOLUTION

S-Properties of Triangle-Objective-S-22-3
S-Properties of Triangle-Objective-S-22-3

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule

P-Properties of Triangle-Objective-S-24-1
P-Properties of Triangle-Objective-S-24-1

SOLUTION

S-Properties of Triangle-Objective-S-24-1
S-Properties of Triangle-Objective-S-24-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of solving trigo n quadratic inequalities

P-Properties of Triangle-Objective-S-25-1
P-Properties of Triangle-Objective-S-25-1

SOLUTION

S-Properties of Triangle-Objective-S-25-1
S-Properties of Triangle-Objective-S-25-1
S-Properties of Triangle-Objective-S-25-2
S-Properties of Triangle-Objective-S-25-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule and conditions of cyclic quadrilateral

P-Properties of Triangle-Objective-S-26-1
P-Properties of Triangle-Objective-S-26-1

SOLUTION

S-Properties of Triangle-Objective-S-26-1
S-Properties of Triangle-Objective-S-26-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius for regular polygon

P-Properties of Triangle-Objective-S-27-1
P-Properties of Triangle-Objective-S-27-1

SOLUTION

S-Properties of Triangle-Objective-S-27-1
S-Properties of Triangle-Objective-S-27-1
S-Properties of Triangle-Objective-S-27-2
S-Properties of Triangle-Objective-S-27-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of inverse trigo functions and how we get  sum of inverse trigonometric series

P-Properties of Triangle-Objective-S-28-1
P-Properties of Triangle-Objective-S-28-1

SOLUTION

S-Properties of Triangle-Objective-S-27-2
S-Properties of Triangle-Objective-S-27-2
S-Properties of Triangle-Objective-S-28-2
S-Properties of Triangle-Objective-S-28-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius

P-Properties of Triangle-Objective-S-29-1
P-Properties of Triangle-Objective-S-29-1

SOLUTION

S-Properties of Triangle-Objective-S-29-1
S-Properties of Triangle-Objective-S-29-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius

P-Properties of Triangle-Objective-M-30-1
P-Properties of Triangle-Objective-M-30-1

SOLUTION

S-Properties of Triangle-Objective-M-30-1
S-Properties of Triangle-Objective-M-30-1
S-Properties of Triangle-Objective-M-30-2
S-Properties of Triangle-Objective-M-30-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of Cos rule

P-Properties of Triangle-Objective-M-31-1
P-Properties of Triangle-Objective-M-31-1

SOLUTION

S-Properties of Triangle-Objective-M-31-1
S-Properties of Triangle-Objective-M-31-1
S-Properties of Triangle-Objective-M-31-2
S-Properties of Triangle-Objective-M-31-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of plane and line in vectors nd 3d 

P-Properties of Triangle-Objective-M-32-1
P-Properties of Triangle-Objective-M-32-1

SOLUTION

S-Properties of Triangle-Objective-M-32-1
S-Properties of Triangle-Objective-M-32-1
S-Properties of Triangle-Objective-M-32-2
S-Properties of Triangle-Objective-M-32-2
S-Properties of Triangle-Objective-M-32-3
S-Properties of Triangle-Objective-M-32-3
S-Properties of Triangle-Objective-M-32-4
S-Properties of Triangle-Objective-M-32-4
S-Properties of Triangle-Objective-M-32-5
S-Properties of Triangle-Objective-M-32-5

PROBLEM

To understand this question of properties of triangles you must know;  The concept  half angle results

P-Properties of Triangle-Objective-M-33-1
P-Properties of Triangle-Objective-M-33-1

SOLUTION

S-Properties of Triangle-Objective-M-33-1
S-Properties of Triangle-Objective-M-33-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of half angle results, Tan or Naiper rule  and area of triangle

P-Properties of Triangle-Objective-M-34-1
P-Properties of Triangle-Objective-M-34-1

SOLUTION

S-Properties of Triangle-Objective-M-34-1
S-Properties of Triangle-Objective-M-34-1
S-Properties of Triangle-Objective-M-34-2
S-Properties of Triangle-Objective-M-34-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius

P-Properties of Triangle-Objective-M-34-1
P-Properties of Triangle-Objective-M-34-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius

P-Properties of Triangle-Objective-M-36-1
P-Properties of Triangle-Objective-M-36-1

SOLUTION

S-Properties of Triangle-Objective-M-36-1
S-Properties of Triangle-Objective-M-36-1
S-Properties of Triangle-Objective-M-36-2
S-Properties of Triangle-Objective-M-36-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of angular bisector and sine rule 

P-Properties of Triangle-Objective-M-37-1
P-Properties of Triangle-Objective-M-37-1

SOLUTION

S-Properties of Triangle-Objective-M-37-1
S-Properties of Triangle-Objective-M-37-1
S-Properties of Triangle-Objective-M-37-2
S-Properties of Triangle-Objective-M-37-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of sine rule and conditions for existence of triangle

P-Properties of Triangle-Objective-M-38-1
P-Properties of Triangle-Objective-M-38-1

SOLUTION

S-Properties of Triangle-Objective-M-38-1
S-Properties of Triangle-Objective-M-38-1
S-Properties of Triangle-Objective-M-38-2
S-Properties of Triangle-Objective-M-38-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius and conditions when two circles touch each other

P-Properties of Triangle-Objective-M-39-1
P-Properties of Triangle-Objective-M-39-1

SOLUTION

S-Properties of Triangle-Objective-M-39-1
S-Properties of Triangle-Objective-M-39-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of circles and basic properties of circles

P-Properties of Triangle-Objective-M-40-1
P-Properties of Triangle-Objective-M-40-1

SOLUTION

S-Properties of Triangle-Objective-M-40-1
S-Properties of Triangle-Objective-M-40-1
S-Properties of Triangle-Objective-M-40-2
S-Properties of Triangle-Objective-M-40-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  area and length of diagonal for square

P-Properties of Triangle-Objective-M-41-1
P-Properties of Triangle-Objective-M-41-1

SOLUTION

 

S-Properties of Triangle-Objective-M-41-1
S-Properties of Triangle-Objective-M-41-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius ,excircle and exradii

P-Properties of Triangle-Objective-M-42-1
P-Properties of Triangle-Objective-M-42-1

SOLUTION

S-Properties of Triangle-Objective-M-42-1
S-Properties of Triangle-Objective-M-42-1
S-Properties of Triangle-Objective-M-42-2
S-Properties of Triangle-Objective-M-42-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius and basic trigo inequalities

P-Properties of Triangle-Objective-M-43-1
P-Properties of Triangle-Objective-M-43-1

SOLUTION

S-Properties of Triangle-Objective-M-43-1
S-Properties of Triangle-Objective-M-43-1
S-Properties of Triangle-Objective-M-43-2
S-Properties of Triangle-Objective-M-43-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept of basic solving trigo equations and exponents

P-Properties of Triangle-Objective-M-44-1
P-Properties of Triangle-Objective-M-44-1

SOLUTION

S-Properties of Triangle-Objective-M-43-2
S-Properties of Triangle-Objective-M-43-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of  sine rule ,cos rule and simple trigo inequalities

P-Properties of Triangle-Objective-M-45-1
P-Properties of Triangle-Objective-M-45-1

SOLUTION

S-Properties of Triangle-Objective-M-45-1
S-Properties of Triangle-Objective-M-45-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept of solving simple trigo equations

P-Properties of Triangle-Objective-M-46-1
P-Properties of Triangle-Objective-M-46-1

SOLUTION

S-Properties of Triangle-Objective-M-46-1
S-Properties of Triangle-Objective-M-46-1
S-Properties of Triangle-Objective-M-46-2
S-Properties of Triangle-Objective-M-46-2

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius

P-Properties of Triangle-Objective-M-47-1
P-Properties of Triangle-Objective-M-47-1

SOLUTION

S-Properties of Triangle-Objective-M-47-1
S-Properties of Triangle-Objective-M-47-1
S-Properties of Triangle-Objective-M-47-2
S-Properties of Triangle-Objective-M-47-2
S-Properties of Triangle-Objective-M-47-3
S-Properties of Triangle-Objective-M-47-3

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of orthocente and lines of equations

P-Properties of Triangle-Objective-M-48-1
P-Properties of Triangle-Objective-M-48-1

SOLUTION

S-Properties of Triangle-Objective-M-48-1
S-Properties of Triangle-Objective-M-48-1

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of sine rule  and ex-centres and exradii

P-Properties of Triangle-Objective-M-49-1
P-Properties of Triangle-Objective-M-49-1

SOLUTION

S-Properties of Triangle-Objective-M-49-1
S-Properties of Triangle-Objective-M-49-1
S-Properties of Triangle-Objective-M-49-2
S-Properties of Triangle-Objective-M-49-2
S-Properties of Triangle-Objective-M-49-3
S-Properties of Triangle-Objective-M-49-3
S-Properties of Triangle-Objective-M-49-4
S-Properties of Triangle-Objective-M-49-4

PROBLEM

To understand this question of properties of triangles you must know;  The concept  of cos rule

P-Properties of Triangle-Objective-M-50-1
P-Properties of Triangle-Objective-M-50-1

SOLUTION

S-Properties of Triangle-Objective-M-50-1
S-Properties of Triangle-Objective-M-50-1

 

Solution-of-Triangle-objectives-12-Trigonometry-IIT JEE MATHS-Mains / Advanced

To understand this question of properties of triangles you must know;  The concept  of incircle  and in-radius, cicumcircle and circumradius

PROBLEM

P-Properties of Triangle-Objective-S-12-1
P-Properties of Triangle-Objective-S-12-1

SOLUTION

S-Properties of Triangle-Objective-S-12-1
S-Properties of Triangle-Objective-S-12-1

Solution-of-Triangle-objectives-11-Trigonometry-IIT JEE MATHS-Mains / Advanced

To understand this question of properties of triangles you must know;  The concept  of circum-centre and circum-radius and sine rule

PROBLEM

P-Properties of Triangle-Objective-S-11-1
P-Properties of Triangle-Objective-S-11-1

SOLUTION

S-Properties of Triangle-Objective-S-11-1
S-Properties of Triangle-Objective-S-11-1