In the given figure, PA and PB are tangents to the given circle such t

1.	In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60° . The length of chord AB is(a) 5√2 cm(b) 5 cm(c) 5√3 cm(d) 7.5 cm
Answer» Correct answer is (b) 5 cm 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° \(\Rightarrow\) x + x + 60° = 180° \(\Rightarrow\) 2x = 180° - 60° \(\Rightarrow\) 2x = 120° \(\Rightarrow\) x = 60° ∴ Each angle of △PAB is 60° and therefore, it is an equilateral triangle. ∴ AB = PA = PB = 5 cm ∴ The length of the chord AB is 5 cm.

In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60° . The length of chord AB is(a) 5√2 cm(b) 5 cm(c) 5√3 cm(d) 7.5 cm

Answer»

Correct answer is (b) 5 cm

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°

\(\Rightarrow\) x + x + 60° = 180°

\(\Rightarrow\) 2x = 180° - 60°

\(\Rightarrow\) 2x = 120°

\(\Rightarrow\) x = 60°

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

∴ AB = PA = PB = 5 cm

∴ The length of the chord AB is 5 cm.

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In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60° . The length of chord AB is(a) 5√2 cm(b) 5 cm(c) 5√3 cm(d) 7.5 cm

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