Question

A chord 12 cm long subtends an angle of 40 degrees at the center of the circle. Calculate the radius of the circle

Answer 1

To calculate the radius of the circle, we first need to use the formula relating the chord length, radius, and the central angle:

Chord length = 2 * radius * sin(angle/2)

Given that the chord length is 12 cm and the central angle is 40 degrees, we can plug these values into the formula to solve for the radius:

12 = 2 * radius * sin(40/2)
12 = 2 * radius * sin(20)
12 = 2 * radius * 0.3420
radius = 12 / (2 * 0.3420)
radius = 17.54 cm

Therefore, the radius of the circle is 17.54 cm.