In the given figure, ACDB is the diameter of the circle such that AC=CD=DB. Three semicircles are drawn by taking AC,CD,and DB as diameters. What is the ratio of the area of shaded portion to the area of non-shaded portion?

Explanation

Area of shaded region=`pi/2(AB)^2/4-pi/2((AB)/3*1/2)^2`.

Area of non shaded region=`pi/2((AB)/2)^2+pi/2((AB)/3*1/2)^2`

Ratio=shaded/non shaded.

=`(pi/2(AB)^2/4-pi/2((AB)/3*1/2)^2)/(pi/2((AB)/2)^2+pi/2((AB)/3*1/2)^2)`

=`4/5`.