SSC CGL 2025 Tier-I · 23 September 2025, Shift 1 · Quantitative Aptitude · Question 24 of 100

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.

Where this paper and its answers come from

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.

If the angle subtended by a chord at the center is150°, what is the angle subtended at a point on the circle in the same segment?

(a)75°
(b)90°
(c)135°
(d)180°

Answer

Why

Correct — A.
Rule: a point on the circle sees a chord at half the angle the chord makes at the centre.

Central angle = 150°
Angle at the circumference = 150° ⁄ 2 = 75° → option (a).

Why the others are wrong

(b)
90° — 90° is the angle in a semicircle. It needs the chord to be a diameter, a central angle of 180°, not 150°.
(c)
135° — 135° fits neither segment. This chord is seen at 75° from the major segment and at 180° − 75° = 105° from the minor one.
(d)
180° — An angle at a point on the circle is always less than 180°. At 180° the point would lie on the chord's own line, which meets the circle only at the chord's two ends.

Concept

The minor arc cut off by this chord makes 150° at the centre. Any point on the major arc sees the chord at half of that, and every such point sees the same angle: angles in the same segment are equal.

The angles in the two segments add to 180°, 75° + 105°, because a point from each segment and the chord's ends form a cyclic quadrilateral.

'In the same segment' is read as the major segment, the side of the chord where the centre lies. A point in the minor segment sees the chord at 105°, which is not offered, so the options confirm the reading.

Key facts

Angle at the circumference = ½ × angle at the centre on the same arc.
Angles in the same segment are equal.
The angles a chord makes in its two segments add to 180°, here 75° + 105°.
For a central angle under 180°, the centre lies in the major segment.

Study next

Reflex central angles and the angle in the minor segmentAlternate segment theorem: the tangent–chord angle equals the angle in the alternate segmentCyclic quadrilateral: opposite angles add to 180°

Common traps

Reporting the central angle, 150°, as the angle at the circumference. Halve it.
Using the minor segment, which gives 105°. The keyed 75° is the major-segment reading.

The half-angle step is keyed at 24 Sep 2025, 12:30, Quant Q.24 (60° at the centre → 30° on the major arc). 23 Sep 2025, 16:00, Quant Q.23 runs it backwards (110° at the circumference → 220°), and 23 Sep 2025, 16:00, Quant Q.24 tests angles in the same segment (50° at C → 50° at D).

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.