geometry

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.

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asked by Lyssa
  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

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