Question

A chord of a circle is 10 cm long. If the circle has a radius of 12 m, calculate the angle subtended at the circumference of a circle.

Answer 1

The angle subtended by a chord at the circumference of a circle is double the angle subtended at the center of the circle.

First, we need to convert the chord length to meters:
10 cm = 0.1 m

Since the chord is a diameter of the circle, it divides the circle into two equal halves. Therefore, the angle subtended at the center of the circle is:

Angle = 2 * arctan((0.1/2) / 12)
≈ 0.16 radians

To find the angle subtended at the circumference of the circle, we multiply the angle by 2:
Angle = 0.16 * 2
Angle ≈ 0.31 radians

Therefore, the angle subtended at the circumference of the circle is approximately 0.31 radians.