Ex 12.3, 9
In figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.
Area of shaded region
= Area of circle with diameter OD
+ Area of semicircle ACB
Area of triangle ABC
Area of circle with diameter OD
Since OD & OA are radius of circle with centre O
OD = OA = 7 cm
Diameter = OD = 7 cm
radius = r = /2 = 7/2 cm
Area of circle with diameter OD = r2
= 22/7 (7/2)^2
= 22/7 7/2 7/2
= 77/2 cm2
Area of circle with diameter OD = 77/2 cm2
Area of semicircle ACB
Diameter = AB
So, radius = OA = 7 cm
Area of semicircle ACB = 1/2 Area of circle
= 1/2 r2
= 1/2 22/7 7 7
= 11 7
= 77 cm2
So, Area of semicircle with diameter AB = 77 cm2
Area ABC
Given that diameters AB & CD are perpendicular
So, AB DC
BOC = AOC = 90
Area ABC = 1/2 Base Height
Here, Base = AB = 2 radius = 2OA = 2 7 = 14
& Height = OC = 7 cm
Putting values
Area ABC = 1/2 Base Height
= 1/2 AB OC
= 1/2 14 7
= 49 cm2
Area of shaded region
= Area of circle with diameter OD
+ Area of semicircle with diameter AB Area of triangle ABC
= 77/2 + 77 49
= 77/2 + 28
= (77 + 2 28)/2
= 133/2
= 66.5

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.