1.

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

Answer»

Given, a circle inscribed in △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=3+5=8cm
∴ the length of BC is 8cm



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