2021 USAJMO Problems/Problem 2
Revision as of 14:00, 15 April 2021 by Leonard my dude (talk | contribs)
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