The circles $x^2 + y^2 - 10x + 16 = 0$ and $x^2 + y^2 = r^2$ intersect at two distinct points if:
Step-by-Step Solution
Key Concept: $C_1 = (5, 0)$, $r_1 = 3$; $C_2 = (0, 0)$, $r_2 = r$; $d = 5$. Two intersections iff $|r - 3| < 5 < r + 3$, i.e., $2 < r < 8$.
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Correct Answer: (1)