SSC CGL 2024 Tier-I · 18 September 2024, Shift 3 · Quantitative Aptitude · Question 23 of 98

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.

If we extend a chord infinitely on both sides, then the chord becomes a _____________.

(a)normal
(b)tangent
(c)secant
(d)diameter

Answer

Why

Correct — C. A chord is the segment joining two points of the circle. Extending it past both ends turns the segment into a full line, but it still meets the circle at those same two points.

Rule: a line that cuts a circle at two distinct points is a secant.

The two intersection points are unchanged by the extension, so the count stays two and the line is a secant → option (c).

Read it the other way round and the pair is easier to keep: the chord is the piece of the secant that lies inside the circle.

Why the others are wrong

(a)
normal — A normal to a circle is the line perpendicular to the tangent at the point of contact, and it passes through the centre. An ordinary chord's extension need not go near the centre.
(b)
tangent — A tangent meets the circle at exactly one point. Extending a chord keeps both endpoints on the circle, so the count is two.
(d)
diameter — A diameter is itself a chord — the longest one, passing through the centre. Extending an ordinary chord does not move it onto the centre, so this cannot be the general answer.

Concept

Circle vocabulary is settled by how many points the line shares with the circle.

Zero points: the line misses the circle. One point: tangent. Two points: secant.

The chord is not a fourth kind of line at all — it is the segment of a secant that lies inside the circle. That is why extending a chord produces a secant rather than something new.

The tangent is the limiting case: slide a secant outwards until its two points merge, and it becomes a tangent.

This item carries no calculation. SSC tests circle definitions as plainly as it tests circle theorems, and the four words offered here — normal, tangent, secant, diameter — are the standard set.

Key facts

A secant is a line that intersects a circle at two distinct points.
A chord is the segment of a secant lying inside the circle.
A tangent touches a circle at exactly one point.
A diameter is a chord through the centre and is the longest chord of a circle.

Study next

The tangent-secant relation PT² = PA × PB from an external pointThe intersecting-chords theorem for two chords meeting inside a circleThe alternate segment theorem, which links a tangent to the angle in the far segment

Common traps

Choosing diameter because it is the only other word on the list that names a chord.
Confusing normal with tangent — the normal is perpendicular to the tangent at the point of contact.
Assuming an extended chord must pass through the centre.

SSC asks the definitions directly, as in "the distance between the longest chord and the centre of a circle is" at 23 Sep 2024, 12:30, Quant Q.17.

It then puts the same vocabulary to work in calculation — a secant PAB drawn from an external point P at 26 Sep 2024, 16:00, Quant Q.25, and a secant from a point 18 cm outside the centre at 19 Sep 2024, 09:00, Quant Q.15, which asks for the radius.

Related PYQs

No directly related past PYQ was found.