If the length of direct common tangent and transverse common tangent of two circles with integral radii are 3 units and 1 unit respectively, then the reciprocal of the square of the distance between the centres of the circles is equal to

Question

If the length of direct common tangent and transverse common tangent of two circles with integral radii are 3 units and 1 unit respectively, then the reciprocal of the square of the distance between the centres of the circles is equal to,

MARKS App · Accepted Answer

Let two circles are of radii r 1 & r 2 and with centres C 1 & C 2 respectively, then C 1 C 2 2 - r 1 - r 2 2 = 9 & C 1 C 2 2 - r 1 + r 2 2 = 1 ⇒ 4 r 1 r 2 = 8 ⇒ r 1 r 2 = 2 Assume, r 1 = 2 & r 2 = 1 Then, C 1 C 2 2 = 1 + 3 2 = 10 1 C 1 C 2 2 = 0.1

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