SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 17 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

The distance between the longest chord and the centre of a circle is:

(a)equal to the diameter
(b)equal to the radius
(c)equal to the half of the radius
(d)equal to zero unit

Answer

Why

Correct — D. The longest chord of a circle is the diameter, and every diameter passes through the centre.

The distance from a point to a line is measured along the perpendicular from that point. Here the line already contains the centre, so that perpendicular has zero length.

Distance = 0 → option (d), equal to zero unit.

The chord formula agrees: a chord at distance d has length 2√(r² − d²), which is largest exactly when d = 0, giving 2r.

Why the others are wrong

(a)
equal to the diameter — The diameter is the chord itself, not a distance. A line that far from the centre misses the circle completely, since no chord lies further out than the radius.
(b)
equal to the radius — At a distance equal to the radius the line touches the circle at a single point. That is a tangent, and it cuts no chord at all.
(c)
equal to the half of the radius — At d = r⁄2 the chord measures 2√(r² − r²⁄4) = r√3 ≈ 1.73r, shorter than the diameter 2r, so that chord is not the longest one.

Concept

A chord at perpendicular distance d from the centre of a circle of radius r has length 2√(r² − d²), because the perpendicular from the centre bisects the chord and makes a right triangle with legs d and half the chord.

That length shrinks as d grows: it is 2r when d = 0, and 0 when d = r, where the line becomes a tangent.

So the longest chord is the one through the centre — the diameter — and its distance from the centre is zero.

The option is worded equal to zero unit rather than 0 cm because the question fixes no radius. The distance is zero whatever the size of the circle.

Key facts

A chord at distance d from the centre of a circle of radius r has length 2√(r² − d²).
The chord is longest at d = 0, where it is the diameter 2r.
At d = r the line touches the circle at one point and is a tangent, not a chord.
The perpendicular from the centre to a chord bisects that chord.

Study next

Computing a chord length from its distance to the centre, and the reverseEqual chords are equidistant from the centre, and the converseTwo parallel chords, where the distances add or subtract depending on the side

Common traps

Reading longest chord as the longest chord that is not a diameter.
Answering with the length of the chord instead of its distance from the centre.
Choosing the radius, which is the distance at which the line stops cutting the circle.

A definition item like this is one line of theory, and the same relation is set as arithmetic elsewhere.

A chord 10 cm from the centre of a circle of radius 5√13 cm is asked at 10 Sep 2024, 12:30, Quant Q.23 (chord 30 cm), and a 32 cm chord 12 cm from the centre at 18 Sep 2024, 09:00, Quant Q.25 (radius 20 cm).

Related PYQs

No directly related past PYQ was found.