2021 USAMO Problems/Problem 1
Rectangles and are erected outside an acute triangle Suppose thatProve 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)
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