Big Book Test 17 Sec 3 Q6

Is there a way to find the overlapping part of the circles or only partially using equilateral triangles? Is that even important? Or is there a an obvious concept / theorem they’re testing here that I should know?

I got the answer right but I’m not confident about this problem. Any help would be great in understanding this better.

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Is there an easier way to do this?

How would you do it?

I was trying to eyeball it, but I am not sure if that is the correct approach.

It seems the shaded area is more than half of area of a semi-circle. By that logic, answer should be A.

Skeptical about this approach, as geometry figures are more than what meets the eye.

In this particular case, that is not a bad idea. And there indeed is a one-liner to do this one. Notice that the area of the shaded region is greater than half the circle. This means that twice the area of the shaded region must be greater than the area of one of the circles.

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Got it thanks!