Art of Problem Solving

AoPS Online

2025 SSMO Speed Round Problems/Problem 2

Revision as of 11:09, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>A</math> and <math>B</math> be points such that <math>AB = 50</math>. Points <math>M</math> and <math>N</math> lie on <math>\overline{AB}</math> such th...")

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $A$ and $B$ be points such that $AB = 50$ . Points $M$ and $N$ lie on $\overline{AB}$ such that $M$ lies between points $A$ and $N$ and $N$ lies between points $B$ and $M$ . Given that $MN = 20$ and $AN \cdot BM$ is maximized, find the length of $AM$ .

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_SSMO_Speed_Round_Problems/Problem_2&oldid=260022"

© 2025 AoPS Incorporated