# 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

NAPIER’S ANALOGY (TANGENT RULE)

COSINE RULE

In a triangle ABC

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

.m-n THEOREM

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

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

BISECTORS OF THE ANGLES

If AD bisects the angle A and divide the base into portions x and y, we have, by Geometry,

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

The distances Between the special points

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.

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

Inscribed & Circumscribed Polygons

(Important Formulae)

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.