Points A and C lie on the circumference of the circle with center O. Angle AOC is 45 degrees and the radius of the circle is 8, what is he length of minor arc AC?

Question

the answer choices are....

1. pi

2. 2pi

3. 3pi

4. 4pi

5. 6pi

Answer 1

Angle 45 degrees is 45/360=1/8 part of the complete revolution of 360 degrees, so the length of the arc subtending 45 degrees at the centre will be 1/8 the circumference of the circle, 1/8 of 2(pi)r, where r is the radius 8=1/8*16(pi)=2(pi) (answer 2).