P and Q are centres of two circles whose radii are 7 cm and 3 cm, respectively. If the direct common tangents to the circles meet PQ extended at A, then A divides PQ ________.

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Accepted Answer

Let the centres of the circles be P (radius 7 cm) and Q (radius 3 cm). The direct common tangents to the circles meet PQ extended at point A. The property of direct common tangents is that the point of intersection (A) divides the line joining the centres (PQ) externally in the ratio of the radii of the circles.

Let AP / AQ = r1 / r2 (externally), where r1 > r2.
Here, r1 = 7 cm (radius at P), r2 = 3 cm (radius at Q).

So, A divides PQ externally in the ratio 7 : 3.

Therefore, the correct answer is: externally in the ratio 7 : 3.

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