Difference between revisions of "2021 AIME II Problems/Problem 12"
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==Problem== | ==Problem== | ||
| − | + | A convex quadrilateral has area <math>30</math> and side lengths <math>5, 6, 9,</math> and <math>7,</math> in that order. Denote by <math>\theta</math> the measure of the acute angle formed by the diagonals of the quadrilateral. Then <math>\tan \theta</math> can be written in the form <math>\tfrac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m + n</math>. | |
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==Solution== | ==Solution== | ||
We can't have a solution without a problem. | We can't have a solution without a problem. | ||
Revision as of 15:57, 22 March 2021
Problem
A convex quadrilateral has area 
and side lengths 
and 
in that order. Denote by 
the measure of the acute angle formed by the diagonals of the quadrilateral. Then 
can be written in the form 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
We can't have a solution without a problem.
See also
| 2021 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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. 
