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Common chord of two intersecting circles: distance between centres or radius

This type of question, asked 2 times: CDS 2 2019, CDS 1 2020. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2019

    87
    Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10310\sqrt{3} cm, then what is the diameter of the circle ?

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  2. Question 2

    CDS 1 2020

    69
    Two circles of radii 20 cm and 16 cm intersect and the length of common chord is 24 cm. If dd is the distance between their centres, then which one of the following is correct ?

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