SSC CGL 2025 Tier-I · 22 September 2025, Shift 1 · Quantitative Aptitude · Question 22 of 98

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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A chord of length 24 cm lies 7 cm away from the center of a circle. What is the approximate radius of the circle?

(a)10 cm
(b)14 cm
(c)17 cm
(d)25 cm

Answer

Why

Correct — B. The perpendicular from the centre bisects the chord, giving a right triangle with the radius as hypotenuse.

Half the chord: 24 ÷ 2 = 12 cm
Pythagoras: r² = 12² + 7² = 144 + 49 = 193
Square root: r = √193 ≈ 13.9 cm

Nearest option: 13.9 rounds to 14 cm → option (b)

Why the others are wrong

(a)
10 cm — 10 cm is shorter than the 12 cm half-chord, yet the radius is the hypotenuse of a triangle with a 12 cm leg. A 20 cm diameter is also too short to hold a 24 cm chord.
(c)
17 cm — 17 cm is too long: 17² = 289, and a 24 cm chord in that circle sits √(289 − 144) = √145 ≈ 12.0 cm from the centre, not 7 cm.
(d)
25 cm — 25 cm comes from using the whole chord: √(24² + 7²) = √625 = 25. The perpendicular meets the chord at its midpoint, so the leg is 12, not 24.

Concept

The perpendicular from the centre to a chord bisects it. The radius to one end of the chord, half the chord and that perpendicular distance form a right triangle:

r² = (half chord)² + (distance)²

The radius is the hypotenuse, so it is always longer than the half-chord. The stem says approximate because 193 is not a perfect square.

7, 24, 25 is a Pythagorean triple, which is why using the whole chord lands on a clean 25 cm. The correct half-chord, 12, does not complete a triple with 7.

Key facts

The perpendicular from the centre of a circle to a chord bisects the chord.
r² = (half chord)² + (distance from centre)².
√193 ≈ 13.89, between 13² = 169 and 14² = 196.

Study next

Two parallel chords on the same side or on opposite sides of the centreEqual chords are equidistant from the centreFinding the chord length from the radius and the distance

Common traps

Using the whole chord, 24, as the leg and getting 25 cm.
Forgetting that the radius must exceed the half-chord, which rules out 10 cm at once.

Whole-number versions of this triangle are on 18 Sep 2024, 09:00, Quant Q.25 (chord 32 cm at 12 cm, keyed radius 20 cm) and 23 Sep 2024, 16:00, Quant Q.3 (chord 14 cm at 24 cm, keyed 25 cm).

26 Sep 2025, 12:30, Quant Q.24 is also approximate: a 20 cm chord 15 cm from the centre, keyed 18 cm.

Related PYQs

No directly related past PYQ was found.

Topic: Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles — all 140 SSC CGL questions on it, every solved shift.