In the given figure, PA and PB are tangents to a circle, such that PA = 8 cm and ∠APB = 60°. The length of the chord AB is
Figure

(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 6 cm

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Solution

(a) 8 cm

Since the lengths of tangents drawn from a point to a circle are equal, PA = PB.
Therefore, $∠$ PAB = $∠$ PBA = x° (say)
Then, x° + x° + 60° = 180°
⇒2x° = 120°
⇒ x° = 60°
∴ Each angle of ΔPAB is 60°; therefore, it is an equilateral triangle.
∴ AB = PA = PB = 8 cm

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