The circles $x^2 + y^2 - 16x - 20y + 164 = r^2$ and $(x - 4)^2 + (y - 7)^2 = 36$ intersect at two distinct points if and only if:
Step-by-Step Solution
Key Concept: $C_1 = (8, 10)$, radius $r$; $C_2 = (4, 7)$, radius $6$; $d = 5$. Two distinct intersections iff $|r - 6| < 5 < r + 6$, i.e., $1 < r < 11$.
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Correct Answer: (2)