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In Figure AB = 36 cm and M is mid-point...

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.

Text Solution

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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`
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