Question

If PA and PB are tangents from an outside point P, such that PA = 10 cm and ∠APB = 60°. Find the length of chord AB.

• A. 8 cm
• B. 9 cm
• C. 10 cm
• D. 11 cm

Answer 1

The correct option is C 10 cm

PA and PB are the tangents from a point P outside the circle with centre O.

PA = 10 cm and ∠APB = 60°

Tangents drawn from a point outside the circle are equal.

PA = PB = 10 cm

∠PAB = ∠PBA

(Angles opposite to equal sides)

But in ∆APB,

∠APB + ∠PAB + ∠PBA = 180° (Sum of angles of a triangle)

=> 60° + ∠PAB + ∠PAB = 180°

=> 2 ∠PAB = 180° – 60° = 120°

∠PAB = 60°

∠PBA = ∠PAB = 60°

PA = PB = AB = 10 cm

Hence, length of chord AB = 10 cm