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A circle of radius r is the smallest circle that cuts both the circles x² + y² = 1 and x² + y² + 8x + 8y - 33 = 0 orthogonally. Find the value of r².
- 7
- 5
- 2
- 10
Correct answer: 7
Solution
The orthogonality conditions force C = 1 and G + F = -4. The radius is minimized when G = F = -2, giving r² = G² + F² - C = 4 + 4 - 1 = 7.
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