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Equal chords: equal distances from the centre, equal central angles, equal arcs

This type of question, asked 3 times: 18 Sep 2024 S2, 24 Sep 2025 S3, 26 Sep 2025 S3. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    18 Sep 2024 S2

    57
    If arcs PAQ and RBS of a circle are congruent, then find the ratio of PQ and RS.

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  2. Question 2

    24 Sep 2025 S3

    74
    In a circle with center O, chords AB and CD are equal in length. If the distance from O to AB is 8 cm, what is the distance from O to CD?

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  3. Question 3

    26 Sep 2025 S3

    72
    Chord AB and chord CD are equal and subtend angles of 50∘50^\circ and x∘x^\circ at the center respectively. Find xx

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