Difference between revisions of "2016 APMO Problems/Problem 1"
(Created page with "==Problem== We say that a triangle <math>ABC</math> is great if the following holds: for any point <math>D</math> on the side <math>BC</math>, if <math>P</math> and <math>Q</...") |
(No difference)
|
Revision as of 21:49, 11 July 2021
Problem
We say that a triangle 
is great if the following holds: for any point 
on the side 
, if 
and 
are the feet of the perpendiculars from to the lines 
and 
, respectively, then the reflection of in the line 
lies on the circumcircle of the triangle . Prove that triangle is great if and only if 
and 
.
