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SMO 2025 Open Round 1 Question 25

SMO · SMO 2025 Open Round 1

Question 25

Let $m$ be the minimum value of the function
$$f(x,y)=\sqrt{x^2+y^2}+\sqrt{x^2-8x+y^2+16}+\sqrt{x^2+y^2-4x-4y+8}.$$
Determine $\lceil m\rceil$.