Exams › SSC CGL (Prelims) › General

In a circle with center O, two chords, PQ and RS, intersect each other at right angles. If the distance from the center O to chord PQ is 5 cm, while the distance from O to chord RS is 12 cm, what is the radius of the circle?

1. 13 cm
2. 17 cm
3. 11 cm
4. 15 cm

Correct answer: 13 cm

Solution

For two chords intersecting at right angles, the perpendicular distances from the center to the chords can be treated as legs of a right triangle whose hypotenuse is the radius. Thus, \(r^2 = 5^2 + 12^2 = 25 + 144 = 169\), so \(r = 13\) cm.

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