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# geometry

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In the diagram, K, O and M are the centers of the three semi-circles. OC = 32 and CB = 38,

What is the area of the semi-circle with center k?

May 5, 2021

### 1+0 Answers

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Consider this labelled diagram

It's given that $$OC=32$$  and $$CB=38$$

$$OB = OC+CB$$

$$=32+38$$

$$=70$$

Radius of semi-circle (3) is $$70$$

And, CB is diameter of semi-circle (2).

So, radius of semi-circle is $$38/2=19$$

From figure, we can infer that

Ar. (semi-circle 1) = Ar. (semi-circle 3) - Ar. (semi-circle 2)

$$= {4900\pi \over 2} - {361\pi \over 2}$$

$$={4539\pi \over 2}$$

$$=7126.23$$ sq. units

Thus, the area of circle with centre K is $$7126.23$$ sq. units.

~Amy

May 5, 2021