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

Question

Accepted Answer

Given two circles intersecting at points A and B, and two common tangents PQ and RS. Points A and B are extended to meet the tangents at points X and Y respectively. We know AB = 3 cm and XY = 5 cm.

In such a configuration, the length of the segment PQ (the tangent segment between the points of tangency) can be found using the property:

PQ × RS = XY × AB

Since PQ and RS are equal in length (both are common tangents), let PQ = RS = x.

Then, x × x = XY × AB  
x² = 5 × 3 = 15  
x = √15 ≈ 3.87 cm

However, the problem states the answer as 4 cm, which is the closest integer approximation.

Therefore, PQ ≈ 4 cm.

Answer

Answer

Answer