Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2017 AIME II Problems/Problem 15

Revision as of 11:39, 23 March 2017 by The turtle (talk | contribs) (Created page with "<math>\textbf{Problem 15}</math> Tetrahedron <math>ABCD</math> has <math>AD=BC=28</math>, <math>AC=BD=44</math>, and <math>AB=CD=52</math>. For any point <math>X</math> in spa...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

$\textbf{Problem 15}$ Tetrahedron $ABCD$ has $AD=BC=28$, $AC=BD=44$, and $AB=CD=52$. For any point $X$ in space, define $f(X)=AX+BX+CX+DX$. The least possible value of $f(X)$ can be expressed as $m\sqrt{n}$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$.

$\textbf{Problem 15 Solution}$

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=2017_AIME_II_Problems/Problem_15&oldid=84877"