Question

In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?

Options

• A. 11

• B. 10

• C. 14

• D. 15

Answer 1

Given, AP = 4 cm, BP = 3 cm and AC = 11 cm.

The lengths of tangents drawn from an external point to the circle are equal.

AP = AR, BP = BQ, CQ = CR …….. (1)

AC = 11 cm

⇒ AR + RC = 11 cm

⇒ AP + CQ = 11 cm [From equation (1)]

⇒ 4 cm + CQ = 11 cm

⇒ CQ = (11 − 4) cm

⇒ CQ = 7 cm

BP = BQ = 3 cm

Now, BC = BQ + QC

⇒ BC = (3 + 7) cm

⇒ BC = 10 cm

Hence, the correct option is B.