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

Question

Philoid · Accepted Answer

In Δ PAB,

∠ APB = 60° and PA = 8 cm [given]

∴ PB = PA = 8 cm

[∵ tangents drawn from an exterior point to the circle are equal in length]

⇒ ∠ PAB = ∠ PBA = θ [LET]

Now, In Δ PAB

∠ APB + ∠ PAB + ∠ PBA = 180° [∵ Sum of all the angles of a Δ is 180°]

⇒ 60° + θ + θ = 180°

⇒ 60° + 2θ = 180°

⇒ 2θ = 120°

∴ θ = 60°

Thus, Δ PAB is an equilateral Triangle.

∴ Length of chord AB = 8 cm.