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.
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
That's easy...
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)
