SSC CGL 2025 Tier-I · 24 September 2025, Shift 2 · Quantitative Aptitude · Question 22 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.

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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.

In a circle, a chord PQ subtends an angle of 50° at point R on the circumference. What is the angle it subtends at point S on the circumference, on the same side as R?

(a)25°
(b)50°
(c)100°
(d)150°

Answer

Why

Correct — B. R and S are on the circle on the same side of chord PQ, so both stand on the same arc PQ.

Double to the centre: ∠POQ = 2 × ∠PRQ = 2 × 50° = 100°
Halve back to S: ∠PSQ = ½ × ∠POQ = ½ × 100° = 50°
Angles in the same segment are equal → option (b)

Why the others are wrong

(a)
25° — 25° halves an angle that is already at the circumference. Halving takes you from the centre (100°) to the circle. Between two points of one segment the angle stays 50°.
(c)
100° — 100° is the angle PQ subtends at the centre, twice the angle at the circumference. S lies on the circle, not at the centre, so it sees half of that: 50°.
(d)
150° — 150° fits no position of S. In R's segment the angle is 50°, and in the opposite segment it is 180° − 50° = 130°.

Concept

An angle at the circumference is half the angle at the centre standing on the same arc. Every point of one segment stands on the same arc, so each sees the chord at the same angle.

That is the theorem: angles in the same segment are equal.

Cross into the other segment and the angle becomes its supplement, since opposite angles of a cyclic quadrilateral add to 180°.

The phrase on the same side as R is what fixes the answer at 50°. A point S on the far side of PQ would see it at 180° − 50° = 130°.

Key facts

Angles in the same segment of a circle are equal.
Angle at the centre = 2 × angle at the circumference on the same arc.
Opposite angles of a cyclic quadrilateral add up to 180°.
The angle in a semicircle is 90°.

Study next

Angle at the centre is twice the angle at the circumferenceCyclic quadrilaterals: opposite angles are supplementaryAlternate segment theorem: the angle between a tangent and a chord

Common traps

Halving or doubling out of habit. Halving is for centre to circumference, and here both points are on the circle.
Ignoring the side. A point on the other arc would give 130°, not 50°.

23 Sep 2025, 16:00, Quant Q.24 is the same item with chord AB and points C and D: 50° at C gives 50° at D on the same arc.

24 Sep 2024, 12:30, Quant Q.24 combines this with the centre rule: PQ subtends 80° at O, so R and S on the major arc each see it at 40°.

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.