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NTA Abhyas JEE Main2020MathematicsCirclePractice

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

Correct answer

0.1

Step-by-step solution

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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