SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 24 of 95

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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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

The diameter of a circle measures 25 cm. What is the maximum length of a chord in this circle?

(a)12 cm
(b)25 cm
(c)50 cm
(d)100 cm

Answer

Why

Correct — B.
Rule: the longest chord of a circle is its diameter, the chord through the centre.

A chord at distance d from the centre has length 2√(r² − d²).
It is largest when d = 0: 2√(r²) = 2r, the diameter.

Diameter given: 25 cm
Longest chord = diameter = 25 cm → option (b)

Why the others are wrong

(a)
12 cm — 12 cm is a possible chord, but it is shorter than the diameter, so it is not the longest. It is not even the radius, which is 12.5 cm.
(c)
50 cm — 50 cm doubles the diameter, as if 25 cm were the radius. The stem gives 25 cm as the diameter, and no chord is longer than that.
(d)
100 cm — 100 cm is four times the diameter. A chord's two endpoints both lie on the circle, so it can never exceed the 25 cm diameter.

Concept

A chord joins two points on a circle. The perpendicular from the centre bisects it, so a chord at distance d from the centre of a circle of radius r has half-length √(r² − d²).

As d shrinks the chord grows, and at d = 0 it passes through the centre and becomes the diameter, 2r. That is why the diameter is the longest chord.

Here r = 12.5 cm. Every chord of this circle is at most 25 cm long, and it reaches 25 cm only when it passes through the centre.

Key facts

The diameter is the longest chord of a circle.
Diameter = 2 × radius, so here r = 12.5 cm.
A chord at distance d from the centre has length 2√(r² − d²).
The perpendicular from the centre to a chord bisects the chord.

Study next

Length of a chord from the radius and its distance from the centreTwo parallel chords on the same side or opposite sides of the centreIntersecting chords: AE × EB = CE × ED

Common traps

Reading the given 25 cm as the radius and doubling it to 50 cm.
Halving the diameter to the radius and picking the nearest option, 12 cm.

The stem gives the diameter and asks for the maximum chord, so recognising the diameter is the whole question. The same fact is asked the other way at 23 Sep 2024, 12:30, Quant Q.17: the longest chord's distance from the centre is zero.

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.