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2 circle of radii 2 and 3 cm touch each other externally. The length of direct common tangent to Tue two circles will be

2 circle of radii 2 and 3 cm touch each other externally. The length of direct common tangent to Tue two circles will be

Grade:9

1 Answers

Vikas TU
14149 Points
3 years ago
Dear Student,
let centres of circles be A and B . AB = 5
       Extend AB to C to intersect direct common tangent PQ at C
By similar triangles CQB and CPA,
BC/(BC+5) = 2/3
  • BC = 10
Similarly, QC/(QC+PQ) = 2/3
We know that QC = √96 by applying Pythagoras th in triangle BQC
Therefore length of Direct common tangent PQ = 2√6 .
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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