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Question

In the figure, B and C are the centres of the 2 circles with radii 9 cm and 3 cm respectively. Also, PQ is the transverse common tangent.
Find the length of PQ, if the centres of circles are 15 cm apart.


  1. 9 cm

  2. 2 cm

  3. 10 cm

  4. 8 cm


Solution

The correct option is A

9 cm


Draw MC MB

PQPB

CQPQ

QPM=PMQ=CQP=90

Since PMCQ is a quadrilateral, sum of angles =360

  MCQ=90   MPQ=PQC=QCM=PMC=90

PMCQ is a rectangle.

PM = QC = 3 cm

PQ = MC

Now, BM = BP + PM = 9 + 3 = 12 cm

In the right angled triangle BMC,

BC2=BM2+MC2

Given, BC = 15

152=122+MC2225=144+MC2225144=(MC)281=(MC)281=MC

MC = 9
MC = PQ = 9
Legth of transverse common tangent = 9 cm.

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