Question

A circle is inscribed in a ΔABC 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 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 = 7 cm, CQ = CR = 5 cm.

Now, BP = (AB – AP)

= (10 – 7)

= 3 cm

∴ BP = BQ = 3cm

∴ BC = (BQ = QC)

⇒ BC = 3 + 5

⇒  BC = 8

∴ The length of BC is 8 cm.

Answer 2

Given, a circle is inscribed in a ΔABC touching AB, BC and AC at P, Q and R respectively.

Since, tangents drawn to a circle from an external point are equal.

∴ AP = AR = 7 cm,

CQ = CR = 5 cm

Now, BP = (AB – AP)

= 10 – 7

= 3 cm

∴ BP = BQ = 3 cm

∴ BC = BQ + QC

= 3 + 5

= 8 cm