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SSC CHSL 2024 PYQ — Question 74

SSC CHSL - 01 July 2024 - Shift 4 • Quantitative Aptitude • Q74

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Two circles of radius 7 units each, intersect in such a way that the common chord is of length 7 units. What is the common area in square units of the intersection?

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Correct answer: D

Explanation

The correct answer option 4 i.e. 98(π6−34)98\big(\frac{\pi}{6}-\frac{\sqrt3}{4}\big).

As seen in the figure

Area of equilateral triangle AOB = √34\frac{√3}{4} × side 2 = √34\frac{√3}{4} × 49

Since AOB is an equilateral triangle, angle AOB = 60º

Hence, the area of the sector OAB = πR2 / 6 = π×496\frac{π × 49}{6}

Hence the required area of intersection = 2[π×496\frac{π × 49}{6} - √34\frac{√3}{4} × 49] = 98(π6−34)98\big(\frac{\pi}{6}-\frac{\sqrt3}{4}\big).