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
As, AB=36 cm (given)
Then, PE = RQ =
⇒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