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.

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

Let

Let p be the center of am and q the centre

To find the area of the shaded region, we can break it down into three parts: the area of the larger semicircle (formed by AB as diameter), the area of the smaller semicircle (formed by AM as diameter), and the area of the circle (formed by the center of the circle that touches all three circles).

Let's calculate the areas step by step:

1. Area of the larger semicircle:
The radius of the larger semicircle is half of AB, which is 36/2 = 18 cm. The area of a semicircle is calculated using the formula: (π * r^2) / 2, where r is the radius.
So, the area of the larger semicircle is (π * 18^2) / 2 = 324π cm^2.

2. Area of the smaller semicircle:
The radius of the smaller semicircle is half of AM, which is half of AB, so it will be 18/2 = 9 cm. Using the same formula as above, the area of the smaller semicircle is (π * 9^2) / 2 = 81π cm^2.

3. Area of the circle:
Since the circle touches all three circles, it is tangent to them. A line drawn from the point of tangency to the center of the larger semicircle will form a right angle with AB. This line will also bisect AB, dividing it into two equal parts. The length of this line is equal to half of AB, which is 18 cm. Thus, the radius of the circle is 18 cm. The area of a circle is calculated using the formula: π * r^2, where r is the radius. Therefore, the area of the circle is π * 18^2 = 324π cm^2.

Now, let's calculate the area of the shaded region:

The shaded region is formed by subtracting the combined areas of the larger semicircle, smaller semicircle, and the circle from the area of the larger semicircle:

Shaded Area = Area of Larger Semicircle - (Area of Smaller Semicircle + Area of Circle)
= 324π - (81π + 324π)
= 324π - 405π
= -81π cm^2

Therefore, the area of the shaded region is -81π cm^2.