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Angles in the same segment are equal

This type of question, asked 3 times: 18 Jul 2023 S3, 23 Sep 2025 S3, 24 Sep 2025 S2. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    18 Jul 2023 S3

    69
    ΔPQR\Delta PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Find the measure of ∠PSQ\angle PSQ.

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  2. Question 2

    23 Sep 2025 S3

    74
    In a circle, chord AB subtends an angle of 50∘50^\circ at a point C on the circle. What is the angle subtended by the same chord AB at another point D on the same arc as C?

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  3. Question 3

    24 Sep 2025 S2

    72
    In a circle, a chord PQ subtends an angle of 50∘50^\circ at point R on the circumference. What is the angle it subtends at point S on the circumference, on the same side as R?

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