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 ________.

P and Q are centers of two circles with radii 7 cm and 3 cm, respectively.

Direct common tangents meet PQ extended at A.

The direct common tangents of two circles divide the line joining their centers externally in the ratio of the radii of the circles.

If the direct common tangents meet the extended line PQ at a point A, this point divides PQ externally in the ratio of the radii of the two circles.

Radius of the circle at P = 7 cm

Radius of the circle at Q = 3 cm

External division by direct common tangents Since the circles are divided by the direct common tangents, the point A divides PQ externally in the ratio of their radii. Hence, the external division ratio is:

Ratio of division = 7:3