2021 USAMO Problems/Problem 1
Rectangles
and
are erected outside an acute triangle
Suppose that
Prove that lines
and
are concurrent.
Solution
Let be the second point of intersection of the circles
and
Then:
Therefore,
is cyclic with diameters
and
, and thus
Similarly,
, meaning points
,
, and
are collinear.
Similarly, the points and
are collinear.
(After USAMO 2021 Solution Notes – Evan Chen)
vladimir.shelomovskii@gmail.com, vvsss
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.