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 which of the following is the length of AP?

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15 cm

10 cm

9 cm

7.5 cm

answer is D.

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Detailed Solution

Consider the given figure,
Question Image

Given,
AP, AQ and BC are tangents to the circle. AB=5 cm, AC=6 cm and BC=4 cm.
We know that tangent segments to a circle from the same external point are congruent. Therefore,

A P = A Q, B P = B D,

and

C Q = C D

.
Calculating the perimeter of the ∆ABC,
Question Image

Calculating the length of AP,

A P + A Q = 15 ⇒ 2 A P = 15 ⇒ A P = 7.5 c m

Hence the length of AP is 7.5cm.
Therefore, option 4 is correct.

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