In the following figure PA and PB are two tangents drawn to a circle with centre O from an external point P such that AP = 5 cm and angle APB =60° find the length of chord AB

Answers 1

The lengths of tangents drawn from a point to a circle are equal.

So, PA = PB and therefore,

∠PAB = ∠PBA = x (say).

Then, in△PAB :

∠PAB + ∠PBA + ∠APB = 180°

=> x + x + 60° = 180°

=> 2x = 180° - 60°

=> 2x = 120°

=> x = 120°/2 = 60°

Each angle of△PAB is 60° and therefore, it is an equilateral triangle.

AB = PA = PB = 5cm

The length of the chord AB is 5cm.

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