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SSC CGL 2023 PYQ — Question 72

SSC CGL - 24 July 2023 - Shift 2 • Quantitative Aptitude • Q72

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The length of the common chord of two circles of radii 15 cm and 13 cm, whose centres are 14 cm apart, is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 24 cm.

Image of two circles with radii r1 and r2, centers O and O', and common chord AB intersecting the line joining the centers at point C

PO = 14 cm, r1 = 13 cm, r2 = 15 cm

Let's assume OC = x, PC = 14 - x

in triangle ACP 

AP2 = PC2 + AC2

⇒ 169 = (14 - x)2 + AC2

⇒ AC2 = 169 - 196 + 28x - x2

⇒ AC2 = -27 + 28x - x2...............(1)

in triangle ACO

AO2 = OC2 + AC2

⇒ 225 = x2 + AC2

⇒ AC2 = 225 - x2..........................(2)

From eq 1 and 2

⇒ -27 + 28x - x2 = 225 - x2

⇒ 28x = 252

x = 252/28 = 9

So, AC2 = 225 - 92 = 144

AC = 12

The length of the common chord = 2 × 12 = 24