Exams › SSC CGL (Prelims) › General

Two circles with centres P and Q have radii 7 cm and 3 cm respectively. Direct common tangents to the circles, when extended, meet at point A on line PQ extended. How does A divide PQ?

1. externally in the ratio 3 : 7
2. externally in the ratio 7 : 3
3. internally in the ratio 7 : 3
4. internally in the ratio 3 : 7

Correct answer: externally in the ratio 7 : 3

Solution

The point where direct common tangents meet is the external centre of similitude. It divides the line joining the centres (PQ) externally in the ratio of their radii: 7 : 3. Division is external because the meeting point lies outside the segment PQ.

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