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The Crescent Moon below is formed by two circles, both of which are tangent to each other. The point E is the center of the larger circle. If BH = 9, and AF = GC = 5AF=GC=5, what is the area of the shaded region?

 

 Jun 12, 2020
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Since FG = 5AF then it's 25, so the diameter of the larger circle is 35.

 

Thus the radius is 17.5, and the HE is 17.5 - 9 = 8.5

 

8.5 + radius = 8.5 + 17.5 = 26

 

26/2 = 13/

 

The larger circle has area of 17.5 ^2 π, and the smaller one has 169π.

 

I will let you solve this on your own.

 

I am not 100 percent sure about  the correctness so if you notice any errors please inform me!

 

If you don't understand feel free to ask!

 Jun 12, 2020

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