Question

the radius of a circle is 12m. You are given is the measure of an angle whose vertex is the center of the circle and whose sides intersect the circle points A and B. Find the shorter distance from A to B along the circle. Give exact answers .

1. 120 degrees

Answer 1

The circumference of the circle is C = 2pi*r. We know that r = 12, so the circumference is C = 2*pi*12 = 24pi


If we draw a picture, we'll see that points A and B lie on the circle and on the angle AOB (O is the center) where m< AOB = 120


It turns out that the distance along the arc AB is exactly 120/360 = 1/3 of the circumference of the circle. This is because we can fit exactly 3 arcs AB along the circle (think of it as a cut and paste job)


So the length of arc AB is (1/3)*24pi = 24pi/3 = 8pi



So the exact length of arc AB is 8pi, which approximates to 25.13274

Answer 2

Oh keep in mind that the units here are in meters, so the approximate answer is 25.13274 meters.