The central angles of arc ACB and arc EFD are the same measure. If AB = 4, BC = 5, and ED = 8, what is the radius of Circle B?

Answer 1

To find the radius of Circle B, we can use the formula for the length of an arc of a circle:

Arc length = radius * central angle

Since the central angles of arc ACB and arc EFD are the same measure, we can set up the equation:

4 + 5 = r * θ
8 = r * θ

To find the central angle, we can use the formula for the central angle of a circle:

Central angle = arc length / radius

The arc length of arc ACB is 4 + 5 = 9, and the arc length of arc EFD is 8. Therefore, the central angle is the same for both arcs:

9 / r = θ
8 / r = θ

Setting these two equations equal to each other, we get:

9 / r = 8 / r

Solving for r, we find:

r = 8

Therefore, the radius of Circle B is 8.