2021 USAJMO Problems/Problem 2
Problem
Rectangles and are erected outside an acute triangle Suppose thatProve that lines and are concurrent.
Solution
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.
~Leonard_my_dude, edited by pear333
See Also
2021 USAJMO (Problems • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAJMO Problems and Solutions |
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