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Question

In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is

(a) 15 cm (b) 10 cm (c) 9 cm (d) 7.5 cm

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Solution

Given: AQ, AP and BC are tangents to the circle with centre O and AB = 5cm , AC =6cm and BC = 4cm.

Let BS = x then CS = 4 – x

As, we know that tangents from an exterior point to a circle are equal in length

⇒AP=AQ

⇒ AB + BP = AC + CQ ........ (1)

BP = BS and CQ = CS .........(2)

from (1) and (2) we get

AB + BS = AC + CS

5+ x = 6 + (4– x)

⇒ x + x = 6+4-5

⇒ 2x = 5

⇒ x = 5/2=2.5

Hence, AP = AB + BP = AB + BS = 5 cm + 2.5 cm = 7.5cm


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