Discussion

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 B and C. Then, the area in sq. cm, of the overlapping region between the two circles is

Explanation:

Since AB is the diameter of the smaller circle ⇒ ∠ACB = 90°.

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In ∆ACB, AC² + BC² = AB² 
⇒ AB = √(8² + 8²) = 8√2

∴ Radius of smaller circle is ½ × 8√2 = 4√2
Diameter of larger circle = 8

Smaller Circle:
Area of green part = 1/2 × π × (4√2)² = 16π

Larger Circle:
Area of blue part = Area of sector CAB – Area of ∆CAB
Area of blue part = 1/4 × π × 8² - 1/2 × 8 × 8 = 16π – 32

∴ Required area = 16π + (16π - 32) = 32(π - 1)

Hence, option (b).

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