Difference between revisions of "2020 AIME II Problems/Problem 15"
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==Problem== | ==Problem== | ||
Let <math>\triangle ABC</math> be an acute scalene triangle with circumcircle <math>\omega</math>. The tangents to <math>\omega</math> at <math>B</math> and <math>C</math> intersect at <math>T</math>. Let <math>X</math> and <math>Y</math> be the projections of <math>T</math> onto lines <math>AB</math> and <math>AC</math>, respectively. Suppose <math>BT = CT = 16</math>, <math>BC = 22</math>, and <math>TX^2 + TY^2 + XY^2 = 1143</math>. Find <math>XY^2</math>. | Let <math>\triangle ABC</math> be an acute scalene triangle with circumcircle <math>\omega</math>. The tangents to <math>\omega</math> at <math>B</math> and <math>C</math> intersect at <math>T</math>. Let <math>X</math> and <math>Y</math> be the projections of <math>T</math> onto lines <math>AB</math> and <math>AC</math>, respectively. Suppose <math>BT = CT = 16</math>, <math>BC = 22</math>, and <math>TX^2 + TY^2 + XY^2 = 1143</math>. Find <math>XY^2</math>. | ||
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| + | ==Solution== | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/bz5N-jI2e0U?t=710 | ||
==See Also== | ==See Also== | ||
{{AIME box|year=2020|n=II|num-b=14|after=Last Problem}} | {{AIME box|year=2020|n=II|num-b=14|after=Last Problem}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 03:46, 8 June 2020
Contents
Problem
Let 
be an acute scalene triangle with circumcircle 
. The tangents to at 
and 
intersect at 
. Let 
and 
be the projections of onto lines 
and 
, respectively. Suppose 
, 
, and 
. Find 
.
Solution
Video Solution
https://youtu.be/bz5N-jI2e0U?t=710
See Also
| 2020 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Problem | |
| 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. 
