Question

Prove: If a chord of a circle has a common end point with a diameter and makes an angle of 30° with it, prove that the distance from the center to the chord is one-fourth the length of the diameter.

Answer 1

Explanation:

The perpendicular distance between the chord and the center of the circle forms a right triangle with the chord and the radius. Using trig:

sin 30° = x / (D/2)

sin 30° = 2x / D

1/2 = 2x / D

x = D/4