Difference between revisions of "2024 AIME I Problems/Problem 14"
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| + | ==problem== | ||
| + | Let <math>ABCD</math> be a tetrahedron such that <math>AB=CD= \sqrt{41}</math>, <math>AC=BD= \sqrt{80}</math>, and <math>BC=AD= \sqrt{89}</math>. There exists a point <math>I</math> inside the tetrahedron such that the distances from <math>I</math> to each of the faces of the tetrahedron are all equal. This distance can be written in the form <math>\frac{m \sqrt n}{p}</math>, where <math>m</math>, <math>n</math>, and <math>p</math> are positive integers, <math>m</math> and <math>p</math> are relatively prime, and <math>n</math> is not divisible by the square of any prime. Find <math>m+n+p</math>. | ||
| + | ==See also== | ||
| + | {{AIME box|year=2024|n=I|num-b=13|num-a=15}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Revision as of 14:09, 2 February 2024
problem
Let 
be a tetrahedron such that 
, 
, and 
. There exists a point 
inside the tetrahedron such that the distances from to each of the faces of the tetrahedron are all equal. This distance can be written in the form 
, where 
, 
, and 
are positive integers, and are relatively prime, and is not divisible by the square of any prime. Find 
.
See also
| 2024 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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. 
