Answer: Choice 4) AC is four times longer than DF
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Explanation:
Let's say AC is 4 units long. This makes AE half as long because AE is a radius of the larger circle and AC is the diameter of that same larger circle. So we know AE = 2. Segment DE is also a radius of that circle. So AE = DE = 2.
Segment DF is half as long as DE, leading to DF = DE/2 = 2/2 = 1.
We have DF = 1 and AC = 4. This shows AC is four times longer than DF.
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Put another way:
AC = 2*(AE)
AC = 2*(DE)
AC = 2*(2*DF)
AC = (2*2)*DF
AC = 4*DF
So AC is four times longer than DF. We can replace DE with 2*DF since the diameter DE is twice as long compared the radius DF (for the smaller circle).
