MathematicsTwo circles touch each other externally. The sum of their areas is  and the distance between their centres is Find the diameters of the circles (in cm).

Two circles touch each other externally. The sum of their areas is  and the distance between their centres is Find the diameters of the circles (in cm).



  1. A
    22, 8
  2. B
    22, 6
  3. C
    26, 8
  4. D
    22, 4 

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    Solution:

    Let us assume the radii of the circles are  Let us draw the figure representing the given information
    https://www.vedantu.com/question-sets/0ab134dc-105e-4115-92d4-80b9c69ad0037131932924003977094.pngWe know that the distance between the centres of two externally touching circles is equal to the sum of the radii of those two circles.
    So, we get  
     We know that the area of the circles is defined as where r is the radius of the circle.
    From the problem, we have From equation (1), we get
    Using the factorisation method, we have
    So, the radii of the circles are 11, 3 cm. We know that the diameter of the circle is twice the radius of that circle.
    So, we get the diameters of the circles as 22, 6 cm
    So, option 2 is correct.
     
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