Difference between revisions of "2021 USAJMO Problems/Problem 2"
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Revision as of 12:18, 16 April 2021
Problem
Rectangles
and
are erected outside an acute triangle
Suppose that
Prove that lines
and
are concurrent.
Solution
We first claim that the three circles
and
are 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
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.