Question

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?
Enter your answer as a number, like this: 42.25


I tried to use the arc length equation and equal them to each other, but I kept getting x=0..... I do not know what to do please help me.

Answer 1

It's just a direct proportion ...
arc EF/6.5 = 6/4 = 3/2
2(arc EF) = 3(6.5)
arc EF = ...

or, you could do your arclength thing: arc = rØ,
for smaller circle:
4Ø = 6.5
Ø = 6.5/4

for larger circle: let arclength EF = x
6Ø = x
Ø = x/6

then
x/6 = 6.5/4
x = 6(6.5)/4 = same as above