Q. 65.0( 2 Votes )

Two circle touch

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 a2 + π b2 = 110………(ii)


Now, a2 + b2 = 35 …….(iii)


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


From equation (i), a = b + 6


Putting this in equation (iii)


(b + 6)2 + b2 = 35


2 b2 + 12 b + 36 = 35


2 b2 + 12 b + 1 = 0


Solving this quadratic equation we get,



Putting this value in (i) we get,


A = b + 6



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