Question

In fig ab=36 cm and m is mid point of ab. Semi circles are drwan on ab, am and mb as diameters. A circle with centre c touches all the three circles. Find the area of shaded region

Answer 1

Answer:

In △COM

(OC)

2

=(CM)

2

+(OM)

2

(x+9)

2

=(18−x)

2

+9

2

x

2

+8x+18r=(18)

2

+x

2

−36x+81

54r=18×18

r=

54

18×18

x=6

Area of shaded region ⇒

2

π(AM)

2

−

2

π(OA)

2

−

2

π(QM)

2

−π(CP)

2

2

π(18)

2

−

2

π(9)

2

−

2

π(9)

2

−π(6)

2

162π−81π−36π

=45π

=141.3 cm

2