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Find the total number of common tangents to the two circles: x² + y² = 4 and x² + y² - 8x + 12 = 0.
- 1
- 2
- 3
- 4
Correct answer: 3
Solution
Circle 1 has centre O1=(0,0) and radius r1=2. Circle 2 rewrites as (x-4)² + y² = 4, centre O2=(4,0), radius r2=2. The distance between centres is 4 = r1+r2, so the circles touch externally. Externally tangent circles have exactly 3 common tangents (2 external + 1 at the point of tangency).
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