Question

Ab is equal to 36 cm and m is the midpoint of a b semi circles are drawn on a b a m and m b as diameter a circle with centre c touches all the three circles find the area of shaded region

Answer 1

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 =1\4×ab=1/4×36=9cm

⇒PR =r + ab \4 = r + 36 \4 = r + 9 = rq

⇒Δ PRQ is n isosceles triangle.
Since, M is the mid-point of PQ, RM ⊥PQ.

Now, MR = CM-CR=1 \2(36) - r = 18 - r

In Δ PMR,

By pythagoras theorem,
Shaded area = Area of semicircle ABC-Area of semicircle AME-Area of semicircle MBD-Area of circle CEDAR