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).

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22, 8

22, 6

26, 8

22, 4

answer is B.

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Detailed 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.png

We 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
Question Image

Using the factorisation method, we have
Question Image

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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