If is the area of the triangle formed by joining the points of contact of the…

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

\Delta_0

is the area of the triangle formed by joining the points of contact of the incircle with the sides of a triangle of area

\Delta

, and

\Delta_1

\Delta_2

, and

\Delta_3

are the corresponding areas for its excircles, prove that

\frac{\Delta_1}{\Delta}+\frac{\Delta_2}{\Delta}+\frac{\Delta_3}{\Delta}-\frac{\Delta_0}{\Delta}=2.