In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle drawn w

Question

In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through Band C. Then the area, in sq. cm, of the overlapping region between the two circles is

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Accepted Answer

32 ( π − 1 ) 32(\pi - 1) 32 ( π − 1 ). BC is the diameter of circle C2 so we can say that ∠ B A C = 90 ∘ \angle BAC=90^{\circ\ } ∠ B A C = 9 0 ∘ as angle in the semi circle is 90 ∘ 90^{\circ\ } 9 0 ∘ Therefore overlapping area = 1 2 \frac{1}{2} 2 1 ​ (Area of circle C2) + Area of the minor sector made be BC in C1 AB= AC = 8 cm and as ∠ B