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 :

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Solution

The correct option is B 10
Given, AP = 4 cm, BP = 3 cm and AC = 11 cm.

The lengths of tangents drawn from an external point to the cirlce 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 ) cm

CQ = 7 cm

BP = BQ = 3 cm

Now, BC = BQ + QC

BC = (3+7) cm

BC = 10 cm

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