How i solve the best solution of ncert class 10 areas related to circles please help me to solve the exercise 12.3 question number 9 . Find the easiest and simplest way to solve this question also find the best solution of this question. In Fig. 12.27, 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.
Radius of larger circle, R = 7 cm
Radius of smaller circle, r = 7/2 cm
Height of ΔBCA = OC = 7 cm
Base of ΔBCA = AB = 14 cm
Area of ΔBCA = 1/2 × AB × OC = (½)×7×14 = 49 cm2
Area of larger circle = πR2 = (22/7)×72 = 154 cm2
Area of larger semicircle = 154/2 cm2 = 77 cm2
Area of smaller circle = πr2 = (22/7)×(7/2)×(7/2) = 77/2 cm2
Area of the shaded region = Area of larger circle – Area of triangle – Area of larger semicircle + Area of smaller circle
Area of the shaded region = (154-49-77+77/2) cm2
= 133/2 cm2 = 66.5 cm2