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Two secants from an external point: PA x PB = PC x PD

This type of question, asked 3 times: 19 Jul 2023 S1, 21 Jul 2023 S1, 23 Sep 2024 S2. All 3 questions below, oldest first.

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  1. Question 1

    19 Jul 2023 S1

    63
    Two chords of a circle, AB‾\overline{AB} and CD‾\overline{CD}, meet outside the circle at the point P. If m(AP‾)=200m(\overline{AP}) = 200 mm, m(AB‾)=120m(\overline{AB}) = 120 mm, and m(CP‾)=160m(\overline{CP}) = 160 mm, what is the length of CD‾\overline{CD} ?

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  2. Question 2

    21 Jul 2023 S1

    52
    In the given figure, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. If CD = 8 cm, PD = 10 cm and PB = 8 cm, find AB.

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  3. Question 3

    23 Sep 2024 S2

    52
    XAB and XCD are two secants to a circle. If XA = 18 cm, AB = 22 cm and XC = 24 cm, then find the value of XD (in cm).

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