Answer :

The figure is given below:

The diagram above shows two circles with centers A and B touching internally at a point.

Let the radius of Circle with Centre A = a and the radius of Circle with center B be b.

It is Given that a – b = 6 ..(i)

And Also the sum of the areas of two circles = 110

Therefore, π a^{2} + π b^{2} = 110………(ii)

Now, a^{2} + b^{2} = 35 …….(iii)

Now we have to Solve (i) and (iii)

From equation (i), a = b + 6

Putting this in equation (iii)

(b + 6)^{2} + b^{2} = 35

2 b^{2} + 12 b + 36 = 35

2 b^{2} + 12 b + 1 = 0

Solving this quadratic equation we get,

Putting this value in (i) we get,

A = b + 6

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