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?
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.