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If one of the diameters of the circle x 2 + y 2 - 2 2 x - 6 2 y + 14 = 0 is a chord of the circle x - 2 2 2 + y - 2 2 2 = r 2 , then the value of r 2 is equal to

Correct answer

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Step-by-step solution

Given that, one of the diameter of the circle x - 2 2 + y - 3 2 2 = 6 is a chord of another circle x - 2 2 2 + y - 2 2 2 = r 2 . Let, C and C 1 be the centres of the circles x - 2 2 + y - 3 2 2 = 6 and x - 2 2 2 + y - 2 2 2 = r 2 respectively. So, C 2 ,   3 2   &   C 1 2 2 ,   2 2 The position of the two circles as shown in figure. Now, C C 1 = 2 2 - 2 2 +   2 2 - 3 2 2 = 2 + 2 = 2 It is clear from the above diagram, ∆ A C C 1 is a right angled triangle. ⇒ r 2 = A C 2 + C C

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