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Angle between two tangents and the angle at the centre add to 180 degrees

This type of question, asked 6 times: 20 Jul 2023 S3, 25 Jul 2023 S2, 9 Sep 2024 S2, 17 Sep 2024 S1, 17 Sep 2025 S3, 19 Sep 2025 S3. All 6 questions below, oldest first.

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  1. Question 1

    20 Jul 2023 S3

    55
    In a circle with centre O, PA and PB are the tangents at A and B, respectively, from an external point P. If ∠APB=24∘\angle APB = 24^\circ , then find ∠AOB\angle AOB.

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  2. Question 2

    25 Jul 2023 S2

    63
    If RP and RQ are two tangents to a circle with centre O such that ∠POQ=120∘\angle POQ = 120^\circ, where P and Q are the points on the circle and R is a point outside the circle then ∠PRQ\angle PRQ is equal to:

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  3. Question 3

    9 Sep 2024 S2

    58
    Let C be a circle with centre O and P be an external point to C. Let PA and PB be two tangents to C with A and B being the points of tangency, respectively. If PA and PB are inclined to each other at an angle of 60∘60^\circ, then find ∠POA\angle POA.

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  4. Question 4

    17 Sep 2024 S1

    66
    AP and AQ are two tangents drawn to a circle with center O from an external point A. If ∠PAQ=40∘\angle PAQ = 40^\circ, then ∠POQ\angle POQ is:

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  5. Question 5

    17 Sep 2025 S3

    74
    When two tangents, PA and PB, are drawn to a circle from a point P outside the circle, and the angle between them is 90∘90^\circ,what is the distance from P to the center (O) of the circle, if the radius is 5 cm?

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  6. Question 6

    19 Sep 2025 S3

    73
    The angle between two tangents drawn from an external point to a circle is 60∘60^\circ. What is the angle subtended by the chord connecting their points of contact at the center?

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