Mathematics Notes - Plane Geometry Problems and Solutions

What is the area of the shaded region on the given figure?
Solution

$three circles inside a circle$

$(2r-a)^2 + r^2 = (a+r)^2$

$4r^2 - 4ra +a^2 +r^2 = a^2 +2ra +r^2$

$4r^2 = 4ra +2ra = 6ra$

$a= \frac{2r}{3}$

The area of the shade region is $A_s = \pi a^2 $

$A_s = \pi (\frac{2r}{3})^2$

$A_s = \frac{4r^2}{9} \pi $ Answer