Question

Help please I'm like struggling ​

Answer 1

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).