PQ and RS are common tangents to two circles intersecting at points 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:
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Use the relationship between lengths of common tangents and chord segments in intersecting circles.
Two circles intersect at points A and B. Common tangents PQ and RS are drawn. Lines through A and B intersect these tangents at points X and Y, respectively. Given that the length of segment AB is 3 cm and the length of segment XY is 5 cm. Using the property of intersecting circles and their common tangents, the length PQ is determined by the formula: \[PQ = \sqrt{XY^2 - AB^2}\] The calculation is as follows: \[PQ = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4 cm\]