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Consider two circles C1: x² + y² = 1 (centre O1=(0,0), radius r1=1) and C2: (x-6)² + y² = 4 (centre O2=(6,0), radius r2=2). Find the length of the direct common tangent of these two circles.

1. sqrt(24)
2. 5
3. sqrt(35)
4. 6

Correct answer: sqrt(35)

Solution

For circles with centres 6 apart and radii 1 and 2, the direct common tangent length is sqrt(d² - (r2-r1)²) = sqrt(36-1) = sqrt(35).

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