PQ and RS are common tangents to two circles intersecting at A and B. A and B, when produced on both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm and XY = 5 cm, then PQ is _______.

AB = 3 cm

XY = 5 cm

Length of common tangent = $$\sqrt{XY^2 - AB^2}$$​​

Solution:  

Using the formula for the length of the common tangent:

PQ = $$\sqrt{XY^2 - AB^2}$$​​

PQ = $$\sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4 \, \text{cm}$$ ​

Thus, the length of PQ is 4 cm.