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Intersecting chords and secant-tangent: PA x PB = PC x PD = PT^2

This type of question, asked 3 times: CDS 1 2021, CDS 1 2025, CDS 2 2025. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2021

    86
    Let PABPAB be a secant to a circle intersecting the circle at AA and BB. Let PTPT be the tangent segment. If PA=9PA = 9 cm and PT=12PT = 12 cm, then what is ABAB equal to?

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  2. Question 2

    CDS 1 2025

    12
    C is the centre of a circle of radius 20 cm. AB is a chord of length 32 cm. E is a point on AB such that CE = 13 cm. What is AE×EBAE \times EB equal to ?

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  3. Question 3

    CDS 2 2025

    87
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : AB and CD are chords of a circle intersecting at P. If AP×PB=48AP \times PB = 48 square units, then what is CP×PDCP \times PD equal to? Statement-I : AP=8AP = 8 units Statement-II : CP=10CP = 10 units Which one of the following is correct in respect of the above Question and the Statements?

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