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?

Question

I really need help cuz if I don`t know the answer I will fail. Please help me please.

Answer 1

EF = 9.75

EF/6 = 6.5/4

the ratio of arc to radius is equal for the two circles

solve for EF

multiply both sides by 6

EF = 6 times 6.5/4 = 9.75

The angle is the ratio of arc to radius. 6.5/4 = 1.625 radians = about 93.1 degrees for each circle

the arc is part of the circumference which is 2(pi)r. since r=4, the circumference is 8pi. the arc 6.5 is 6.5/8pi = 6.5/25.13 = .258 or 25.8% of the circumference. .258 x 360 degrees = 93.1 degrees = 1.625 radians

Multiply the angle, in radians by the radius to get the arc length

1.625 x 4 = 6.5

For a circle with radius 6 the arc length is 1.625 x 6 = 9.75