Question

P and Q are the centres of two circles whose radii are 5 cm and 11 cm, respectively. If the direct common tangent to the circles meets PQ at M, then, M divides PQ in the ratio

5 : 11 internally

11 : 5 internally

5 : 11 externally

11 : 5 externally

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Answer

The correct option is C: 5 : 11 externally

The direct common tangent to two circles divides the line segment joining their centers externally in the ratio of their radii.

Given:

  • Radius of the first circle, ( r_1 = 5 ,\text{cm} )
  • Radius of the second circle, ( r_2 = 11 ,\text{cm} )

Let ( M ) be the point where the tangent meets the line segment ( PQ ), which connects the centers ( P ) and ( Q ) of the two circles.

Thus, ( M ) divides ( PQ ) in the ratio ( 5:11 ) externally.


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