Prove that the coordinates of the incentre of a triangle whose vertices are are (…

MATHEMATICS · Subjective · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Prove that the coordinates of the incentre of a triangle whose vertices are

A(x_1, y_1), B(x_2, y_2), C(x_3, y_3)

are

\left( \frac{ax_1 + bx_2 + cx_3}{a+b+c}, \frac{ay_1 + by_2 + cy_3}{a+b+c} \right)

where,

a, b, c

are the lengths of sides

BC, CA

and

AB

respectively. Also, prove that the internal bisectors of the angles of a triangle are concurrent.