Question

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:

• A. 4 cm
• B. 2 cm
• C. 3 cm
• D. 6 cm

Hint:

Use the relationship between lengths of common tangents and chord segments in intersecting circles.

Answer 1

The Correct Option is A

Given two circles intersect at points A and B. The common tangents PQ and RS are such that when lines through A and B meet tangents at points X and Y, the segment AB = 3 cm and XY = 5 cm.
By the property of intersecting circles and their common tangents, the length PQ can be found using:
\[PQ = \sqrt{XY^2 - AB^2}\]
Calculate:
\[PQ = \sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4 cm\]