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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
Solution
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.
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