2021 USAJMO Problems/Problem 2
Rectangles and are erected outside an acute triangle Suppose thatProve that lines and are concurrent.
We first claim that the three circles and share a common intersection.
Let the second intersection of and be . Then which implies that is cyclic as desired.
Now we show that is the intersection of and Note that so are collinear. Similarly, and are collinear, so the three lines concur and we are done.
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