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
is cyclic with diameters
and
Similarly,
points
and
are collinear.
Similarly, triples of points and
are collinear.
(After USAMO 2021 Solution Notes – Evan Chen)
vladimir.shelomovskii@gmail.com, vvsss
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