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SSC CGL 2025 PYQ — Question 52

SSC CGL - 16 Sep 2025 - Shift 1 • Quantitative Aptitude • Q52

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A chord of a circle has a length of 12 cm. The angle subtended by the chord at a point on the circumference is 30. What is the distance from the center of the circle to the chord?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 636 {\sqrt{3} } cm.

Angle at circumference = 30°

So angle at center = 2 × 30° = 60°

Chord = 2r sin(θ2θ\over2)

⇒ 12 = 2r sin30°

⇒ 12 = 2r × 121\over2

⇒ 12 = r

So, radius = 12 cm

Distance from center to chord(d) = r cos(θ\over2)

⇒ 12 cos30° = 12 × √32√3\over2 = 6√3 cm