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Two circles touching externally, sum of areas and distance between centres given: difference of radii

The same question, asked 3 times: CDS 2 2016*, CDS 2 2021*, CDS 2 2022. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    47
    Two circles touch externally and sum of their areas is 130π cm2130\pi\ \text{cm}^2 and the distance between their centres is 14 cm. What is the difference in the radii of the circles ?

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  2. Question 2

    CDS 2 2021

    62
    Two circles touch externally. The sum of their areas is 41π41\pi square cm. If the distance between their centres is 9 cm, then what is difference between their diameters ?

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  3. Question 3

    CDS 2 2022

    88
    Two circles touch externally. The sum of their areas is 89π89\pi square cm and the distance between their centres is 13 cm. What is the difference in their radii ?

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