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.

Let r = the radius of the circle=CR.

Consider AMB is a straight line such that AM=MB.

Semicircles are drawn with AB,AM and MB as diameters.

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.

As, AB=36 cm (given)

Then, PE = RQ =

⇒PR =

⇒Δ PRQ is n isosceles triangle.

Since, M is the mid-point of PQ, RM ⊥PQ.

Now, MR = CM-CR=

In Δ PMR,

By pythagoras theorem,

Shaded area = Area of semicircle ABC-Area of semicircle AME-Area of semicircle MBD-Area of circle CED

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