From a point P, two tangents PA and PB are drawn to a circle. If the length of the chord AB is equal to the radius of the circle, what is the angle ∠APB?
Show answer & explanation
Correct answer: D
Explanation
Given:
Radius = r
Chord AB = r
PA and PB are tangents
By the formula:
Chord = 2r sin(θ/2)
r = 2r sin(θ/2)
1 = 2 sin(θ/2)
sin(θ/2) = 1/2
θ/2 = 30°
θ = 60°
∠APB = 180° − θ
= 180° − 60°
= 120°