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Two touching circles: sum of areas and distance between centres give the radii

This type of question, asked 5 times: CDS 2 2016, CDS 1 2020, CDS 2 2021, CDS 2 2022, CDS 1 2026. All 5 questions below, oldest first.

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  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 1 2020

    71
    Two circles touch internally. The sum of their areas is 136π136\pi cm2^2 and distance between their centres is 4 cm. What are the radii of the circles ?

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  3. Question 3

    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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  4. Question 4

    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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  5. Question 5

    CDS 1 2026

    75
    A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : Two circles with radii p, q (p>q)(p > q) in cm touch externally, where p, q are natural numbers and each greater than 1. What is the value of (p−q)(p - q) ? Statement-I : The sum of their areas is 130π130\pi cm2\text{cm}^2 Statement-II : The distance between the centres of the two circles is 14 cm Which one of the following is correct in respect of the above Question and the Statements ?

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