Difference between revisions of "2016 APMO Problems/Problem 1"
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Revision as of 20:49, 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
.