In the given figure, the sides AB , BC and CA of triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then length of BC is
(a) 11 cm (b) 10 cm (c) 14 cm (d) 15 cm [CBSE 2012]
It is given that the sides AB , BC and CA of ∆ABC touch a circle at P, Q and R, respectively.
Also, PA = 4 cm, PB = 3 cm and AC = 11 cm
We know that, the lengths of tangents drawn from an external point to a circle are equal.
∴ AR = AP = 4 cm
BQ = BP = 3 cm
Now, CR = AC − AR = 11 cm − 4 cm = 7 cm
∴ CQ = CR = 7 cm (Lengths of tangents drawn from an external point to a circle are equal)
Now,
BC = BQ + CQ = 3 cm + 7 cm = 10 cm
Thus, the length of BC is 10 cm.
Hence, the correct answer is option B.