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…

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 Content Team · Accepted Answer

Correct answer: 0.1. Let two circles are of radii r_1 & r_2 and with centres C_1 & C_2 respectively, then C^1C22-r^(1-r22)=9 & C^1C22-r^(1+r22)=1 ⇒4r_1r_2=8⇒r_1r_2=2 Assume, r_1=2 & r_2=1 Then, C^1C22=1+3^2=10 1/(C^1C22)=0.1

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

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