SSC CGL 2025 Tier-I · 18 September 2025, Shift 1 · Quantitative Aptitude · Question 21 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 cyclic quadrilateral ABCD, AB is the diameter of the circle. If angle ACD is 40°, what is the measure of angle BAD?

(a)40°
(b)50°
(c)80°
(d)90°

Answer

Why

Correct — B. Work in triangle ABD, using two circle facts.

∠ABD = ∠ACD = 40° (same segment: both stand on chord AD)
∠ADB = 90° (AB is a diameter: angle in a semicircle)
∠BAD = 180° − 90° − 40° = 50° → option (b)

Cross-check: ∠ACB = 90°, so ∠BCD = 90° + 40° = 130°, and the opposite angle ∠BAD = 180° − 130° = 50°.

Why the others are wrong

(a)
40° — 40° is ∠ABD, the angle equal to ∠ACD because both stand on chord AD. It sits at vertex B, not at A.
(c)
80° — 80° is double 40°, the angle chord AD subtends at the centre. ∠BAD is an angle at the circumference in triangle ABD, and it comes out as 50°.
(d)
90° — 90° is the angle in a semicircle. The diameter AB makes that right angle at D (∠ADB) and at C (∠ACB), not at A.

Concept

Angles in the same segment are equal: every point on one arc sees a chord at the same angle. So ∠ACD = ∠ABD.

The angle in a semicircle is 90°: any point on the circle sees a diameter at a right angle. So ∠ADB = ∠ACB = 90°.

The cross-check uses a third fact: opposite angles of a cyclic quadrilateral add to 180°.

The question gives no figure. The vertices of a cyclic quadrilateral ABCD are taken in order round the circle, which puts B and C on the same arc of chord AD.

Key facts

Angles subtended by the same chord at points on the same arc are equal.
The angle subtended by a diameter at any point of the circle is 90°.
Opposite angles of a cyclic quadrilateral add to 180°.
The angle a chord subtends at the centre is double the angle it subtends at a point on the major arc.

Study next

Angle between a tangent and a chord (alternate segment theorem)Exterior angle of a cyclic quadrilateral equals the interior opposite angleAngle at the centre versus angle at the circumference

Common traps

Stopping at ∠ABD = 40° and answering it, when the question asks for the angle at A.
Doubling 40° to 80°, which is the angle at the centre, not at vertex A.

The same pairing of a diameter with a cyclic quadrilateral is asked at 19 Sep 2024, 12:30, Quant Q.2: PQ is a diameter and ∠PSR = 120°, so ∠QPR = 180° − 90° − 60° = 30°.

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.