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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
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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 smiley

                               

 May 5, 2021

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