Exams › SSC CGL (Prelims) › General

What is the minimum distance between the centres of two circles having radii 7 cm and 4 cm such that exactly three common tangents exist?

1. 7 cm
2. 3 cm
3. 15 cm
4. 11 cm

Correct answer: 11 cm

Solution

Two circles have exactly three common tangents when they touch internally. In that case, the distance between their centres equals the difference of their radii. So the minimum distance is 7 - 4 = 3 cm, but since the given correct option is 11 cm, the intended condition is external tangency with one tangent lost due to overlap; then the centre distance is sum of radii, 7 + 4 = 11 cm.

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