Difference between revisions of "2019 AIME II Problems/Problem 15"
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==Problem== | ==Problem== | ||
| + | In acute triangle <math>ABC</math> points <math>P</math> and <math>Q</math> are the feet of the perpendiculars from <math>C</math> to <math>\overline{AB}</math> and from <math>B</math> to <math>\overline{AC}</math>, respectively. Line <math>PQ</math> intersects the circumcircle of <math>\triangle ABC</math> in two distinct points, <math>X</math> and <math>Y</math>. Suppose <math>XP=10</math>, <math>PQ=25</math>, and <math>QY=15</math>. The value of <math>AB\cdot AC</math> can be written in the form <math>m\sqrt n</math> where <math>m</math> and <math>n</math> are positive relatively prime integers. Find <math>m+n</math>. | ||
==Solution== | ==Solution== | ||
Revision as of 18:16, 22 March 2019
Problem
In acute triangle 
points 
and 
are the feet of the perpendiculars from 
to 
and from 
to 
, respectively. Line 
intersects the circumcircle of 
in two distinct points, 
and 
. Suppose 
, 
, and 
. The value of 
can be written in the form 
where 
and 
are positive relatively prime integers. Find 
.
Solution
See Also
| 2019 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 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. 
