Circle A has a radius of 4 and arc BD has length of 6.5. Circle C is a different circle with radius 6 and arc EF. Angle ECF is congruent to angle BAD.
What is the length of arc EF?
To find the length of arc EF in circle C, we first need to find the measure of angle ECF.
Since angle ECF is congruent to angle BAD, we can use the formula for the length of an arc:
Length of arc = (angle/360) x 2π x radius
For circle A:
Length of arc BD = (angle BAD/360) x 2π x 4
Given that arc BD has a length of 6.5, we can set up the equation:
6.5 = (angle BAD/360) x 2π x 4
Solving for angle BAD:
6.5 = (angle BAD/360) x 8π
angle BAD = (6.5)/(8π) x 360 = 82.29 degrees
Since angle ECF is congruent to angle BAD, angle ECF is also 82.29 degrees. Now we can find the length of arc EF for circle C using the formula:
Length of arc EF = (angle ECF/360) x 2π x 6
Length of arc EF = (82.29/360) x 2π x 6
Length of arc EF ≈ 4.23
Therefore, the length of arc EF in circle C is approximately 4.23.