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Intersecting chords: AP x PB = CP x PD

This type of question, asked 5 times: 21 Jul 2023 S3, 27 Jul 2023 S1, 11 Sep 2024 S1, 16 Sep 2025 S2, 17 Sep 2025 S2. All 5 questions below, oldest first.

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  1. Question 1

    21 Jul 2023 S3

    53
    Two chords AB and CD of a circle meet inside the circle at point P. If AP = 12 cm, AB = 20 cm and CP = 16 cm, then CD = ?

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  2. Question 2

    27 Jul 2023 S1

    54
    In the following figure, O is the centre of the circle. Its two chords AB and CD intersect each other at point P inside the circle. If AB = 18 cm, PB = 6 cm and CP = 4 cm, then find the measure of PD.

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  3. Question 3

    11 Sep 2024 S1

    61
    In a circle, two chords MN and PQ intersect at O. If MO = 9 cm, ON = 5 cm and OQ = 6 cm, then the value of OP (in cm) is:

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  4. Question 4

    16 Sep 2025 S2

    73
    In a circle, chord AB and chord CD intersect at E such that AE : EB = 2:32 : 3 and CE : ED = 5:25 : 2. If AB = xx and CD = y, which of the following is true?

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  5. Question 5

    17 Sep 2025 S2

    72
    Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?

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