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Angle at the centre is twice the angle at the circumference

This type of question, asked 8 times: 14 Jul 2023 S4, 26 Jul 2023 S1, 24 Sep 2024 S2, 21 Sep 2025 S2, 22 Sep 2025 S3, 23 Sep 2025 S1, 23 Sep 2025 S3, 24 Sep 2025 S2. All 9 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S4

    57
    In the given figure, 'G' is the centre of the circle. Find the angle ACB when ∠AGB=132∘\angle AGB = 132^\circ.

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  2. Question 2

    26 Jul 2023 S1

    55
    In the given figure, O is the centre of the circle and ∠AOB=130∘\angle AOB = 130^\circ. Find ∠APB\angle APB.

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  3. Question 3

    24 Sep 2024 S2

    74
    Let C be a circle with centre O and PQ be a minor arc on C. Let R and S be two points on the major arc of PQ on C. If PQ subtends an angle 80∘80^\circ at O, find ∠PRQ\angle PRQ and ∠PSQ\angle PSQ, respectively.

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  4. Question 4

    21 Sep 2025 S2

    73
    A chord of a circle subtends an angle of 60∘60^\circ at the center. What is the angle subtended at a point on the circle in the same segment?

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  5. Question 5

    22 Sep 2025 S3

    73
    A chord subtends an angle of 70∘70^\circ at the center of a circle. What is the measure of the angle subtended by the same chord at any point on the remaining part of the circle?

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  6. Question 6

    23 Sep 2025 S1

    72
    In a circle, angle subtended by chord AB at the center is 80∘80^\circ. What is the measure of angle ∠\angleACB, where C lies on the circle?

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  7. Question 7

    23 Sep 2025 S1

    74
    If the angle subtended by a chord at the center is 150∘150^\circ, what is the angle subtended at a point on the circle in the same segment?

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  8. Question 8

    23 Sep 2025 S3

    73
    A chord divides a circle into two arcs. The angle subtended by the major arc at the circumference is 110∘110^\circ . What is the central angle subtended by the major arc?

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  9. Question 9

    24 Sep 2025 S2

    74
    In a circle, chord AB subtends an angle of 60∘60^\circ at the center. What is the angle subtended by the same chord AB at any point C on the major arc (opposite side of the center)?

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