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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.
Solution
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)
⇒ BC = 3 + 5
⇒ BC = 8
∴ The length of BC is 8 cm.
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