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In the given figure, PA and PB are tangents to the given circle such that PA=5 cm and ∠APB=60⁰. Then, which of the following is the length of chord AB?

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52 cm

5 cm

53 cm

7.5 cm

answer is B.

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Detailed Solution

Consider the given figure,
Question Image

We know that the lengths of tangents drawn from a point to a circle are equal.
Therefore,

P A = P B

.
So,

∠ P A B = ∠ P B A = x

(say).
Consider

Δ P A B

and apply angle sum property,

⇒ ∠ P A B + ∠ P B A + ∠ A P B = 180 ° ⇒ x + x + 60 ° = 180 ° ⇒ 2 x = 120 ° ⇒ x = 60 °

Each angle of

Δ P A B

60 °

.
Thus, it is an equilateral triangle, i.e.

A B = P A = P B = 5 c m

.
Hence, the length of the chord AB is

5 cm

.
Therefore, option 2 is correct.

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