A point P lies outside a circle with center O and radius r = 6 cm. Two tangents PA and PB are drawn from P to the circle, and the angle between the tangents ∠APB = 60°. What is the distance from point P to the center O?
Show answer & explanation
Correct answer: D
Explanation
radius r = 6 cm
∠APB = 60°
According to the formula:
∠APB = 180° − ∠AOB
OA ⟂ PA
∠AOB = 180° − 60° = 120°
In isosceles triangle AOB,
∠OAB = ∠OBA = (180 − 120)/2 = 30°
In right triangle OAP,
∠OAP = 90°, ∠OBA = 30° ⇒ ∠OPA = 60°
cos60° = OA / OP
1/2 = 6 / OP
OP = 12 cm