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Tangent and secant from an external point, tangent and outer segment given: length of the chord

The same question, asked 2 times: 14 Jul 2023 S1*, 17 Sep 2025 S2. Every wording 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

    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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