Difference between revisions of "2023 AIME I Problems/Problem 12"
R00tsofunity (talk | contribs) (Created page with "==Problem 12== Let <math>ABC</math> be an equilateral triangle with side length <math>55</math>. Points <math>D</math>, <math>E</math>, and <math>F</math> lie on sides <math>B...") |
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==Solution== | ==Solution== | ||
| − | Miquel point | + | Miquel point and law of cosines, answer should be 75 |
==See also== | ==See also== | ||
Revision as of 13:20, 8 February 2023
Problem 12
Let 
be an equilateral triangle with side length 
. Points 
, 
, and 
lie on sides 
, 
, and 
, respectively, such that 
, 
, and 
. A unique point 
inside 
has the property that ![\[\measuredangle AEP=\measuredangle BFP=\measuredangle CDP.\]](http://latex.artofproblemsolving.com/6/7/a/67a713b041de313419e8409414bca88a912a3f2b.png)
Find 
.
Solution
Miquel point and law of cosines, answer should be 75
See also
| 2023 AIME I (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. 
