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Question

In the given figure, ΔABC is circumscribed, touching the circle at P, Q and R. AP = 4 cm, BP = 6 cm, AC = 12 cm and BC = x cm. Find x.


(a) 10 cm
(b) 14 cm
(c) 18 cm
(d) 12 cm

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Solution

(b) 14 cm
Tangents drawn from an external point to a circle are equal.So, AR=AP=4 cmCR=AC-ARCR=12-4 cmCR=8 cmBQ=BP=6 cmBC=BQ+CQBC=6+8 cm [CQ=CR=8 cm]BC=14 cm

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