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Tangent-secant theorem: tangent squared = outer segment x whole secant

This type of question, asked 5 times: 14 Jul 2023 S1, 24 Jul 2023 S1, 26 Jul 2023 S4, 17 Sep 2025 S2, 19 Sep 2025 S3. All 6 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S1

    63
    In the given figure, PABPAB is a secant and PTPT is a tangent to the circle from PP. If PT=8PT = 8 cm, PA=6PA = 6 cm and AB=xAB = x cm, then the value of xx is:

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  2. Question 2

    24 Jul 2023 S1

    75
    DE is a chord and KDE is a secant of a circle. If KD = 9 cm, DE = 7 cm and KH is a tangent to the circle at point H, then find KH.

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  3. Question 3

    26 Jul 2023 S4

    59
    In the figure, PT is a tangent. If TP=12TP = 12 cm, PB=x+7PB = x + 7 cm and PA=xPA = x cm, then find the value of x.

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  4. Question 4

    26 Jul 2023 S4

    63
    Find the value of x in the given figure where TP ( tangent on point T) = 15 cm, PB=2x+3PB = 2x + 3 cm, PA=9PA = 9 cm.

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  5. Question 5

    17 Sep 2025 S2

    68
    A triangle ABC is inscribed in a circle. A tangent is drawn to the circle at point A, intersecting the extension of side BC at D. If AD=6 cm and CD=4 cm, what is the length of side BC?

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  6. Question 6

    19 Sep 2025 S3

    74
    From a point P outside a circle, a tangent PA and a secant PBC are drawn. If PA=6 cm and BC=5 cm, what is the length of the segment PB?

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