Difference between revisions of "2025 AIME I Problems/Problem 14"
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| + | ==Problem== | ||
| + | Let <math>ABCDE</math> be a convex pentagon with <math>AB=14,</math> <math>BC=7,</math> <math>CD=24,</math> <math>DE=13,</math> <math>EA=26,</math> and <math>\angle B=\angle E=60^{\circ}.</math> For each point <math>X</math> in the plane, define <math>f(X)=AX+BX+CX+DX+EX.</math> The least possible value of <math>f(X)</math> can be expressed as <math>m+n\sqrt{p},</math> where <math>m</math> and <math>n</math> are positive integers and <math>p</math> is not divisible by the square of any prime. Find <math>m+n+p.</math> | ||
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| + | ==See also== | ||
| + | {{AIME box|year=2025|num-b=12|num-a=14|n=I}} | ||
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| + | {{MAA Notice}} | ||
Revision as of 20:10, 13 February 2025
Problem
Let 
be a convex pentagon with 
and 
For each point 
in the plane, define 
The least possible value of 
can be expressed as 
where 
and 
are positive integers and 
is not divisible by the square of any prime. Find 
See also
| 2025 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
