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How many common tangents can be drawn to the circles x² + y² = 1 and x² + y² - 2x - 6y + 6 = 0?

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

Circle 1: centre (0,0), r1=1; Circle 2: centre (1,3), r2=2. Distance d = sqrt(10) approx 3.16 > r1+r2 = 3, so the circles are separate and have 4 common tangents.

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