Question

A circle k(O) with radius 4.5 cm is given. Through point A (OA=9 cm) draw two tangents to the circle. What is the measure of the angle between the tangents?

Answer 1

60°

Explanation:

A tangent, together with a radius to the tangent point and segment OA, forms a right triangle with hypotenuse 9 and opposite side 4.5. SOH CAH TOA reminds you that the sine of an agle is the ratio of the opposite side to the hypotenuse of the right triangle.

Thus half the angle at A is the angle whose sine is 4.5/9 = 1/2. That angle is 30°, so the entire angle between the tangents at A is 2·30° = 60°.