Find the lengths of the arcs into which two radii divide the circle if the angle between

Find the lengths of the arcs into which two radii divide the circle if the angle between them is 72 and the radius of the circle is 6.

Determine the length of the circle.

L = 2 * π * R = 2 * π * 6 = 12 * π cm.

Since the inscribed angle AOB, by condition, is equal to 72, then the degree measure of the smaller arc is AB = 72.

Determine what part of the circle is the arc AC.

360/72 = 5.

Then the length of the smaller arc AB = 12 * π / 5 = 2.4 * π cm.

The length of the larger arc AB = 12 * π – 2.4 * π = 9.6 * π cm.

Answer: The lengths of the arcs are 12 * π cm and 2.4 * π cm.