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Point Y lies on line segment XZ such that XY = 2 and YZ = 8.  Semicircles are constructed with diameters XY, XZ, and YZ. Find the area of the blue region.

 

 Jul 25, 2021
 #1
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Area  of  the largest semi-circle  with diameter  10  =   (1/2) pi (5^2)  =  12.5 pi

 

Area  of  semi-circle  with diameter 8  =  (1/2) pi (4^2)  =   8 pi

 

Area of semi-circle  with diameter 2   =   (1/2) pi (1^2)   =   .5 pi

 

Blue Area  =   pi  ( 12.5 -  8 - .5)   =   4 pi  units^2

 

 

cool cool cool

 Jul 25, 2021
 #2
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+1

That's easy...smiley

 

Try this one: what's the area of the largest possible circle that can be inscribed in the purple region?

( Inscribed circle is tangent to all 3 semicircles)

Guest Jul 26, 2021

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