Question

A circle is inscribed in a ΔABC touching AB, BC and AC at P, Q and R respectively. If AB = 10 cm, AR = 7cm and CR = 5cm, find the length of BC.

Answer 1

Given, a circle inscribed in triangle ABC, such that the circle touches the sides of the triangle 

Tangents drawn to a circle from an external point are equal.

∴ AP = AR = 7cm, CQ = CR = 5cm.

Now, BP = (AB - AP) = (10 - 7) = 3cm

∴ BP = BQ = 3cm

∴ BC = (BQ + QC)

\(\Rightarrow\) BC = 3 + 5

\(\Rightarrow\) BC = 8

∴ The length of BC is 8 cm.