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

Answer 1

There is no diagram posted, and not enough description to give a defined question.
I am adding the following guesses. Check if they are correct. If they are not, post the complete description.

AMB is a straight line such that AM=MB.
Semicircles are drawn with AB,AM and MB as diameters. Also, AM=MB=18 cm.

A circle is drawn with centre C such that CM is perpendicular to AB, and such that the circle is tangent to all three semicircles.

We need to find the interstitial space outside of the circle, the two small semi-circles and INSIDE the big semi-circle.

Hints:
Use r to represent the radius of the circle, and express the sides of the right triangle joining the centres of the circle, the large semicircle, and one of the small semicircles. Solve for r and find the areas.
See link:
http://img14.imageshack.us/img14/2479/1356374872.jpg

Answer 2

Let

Answer 3

Let p be the center of am and q the centre