In Figure AB = 36 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of the shaded region.

Explanation

Let the radius of the circle be r.

and `triangle PCM` is right `triangle`

`PC^2=PM^2+MC^2`

`(9+r)^2=(9)^2+(16-r)^2`

`81+r^218r=81+324+r^2-36r`

`54r=324`

`r=324/54=6cm`

`Area of shaded region = (324pi)/2-81pi+36pi`

...