2021 USAMO Problems/Problem 6
Problem 6
Let be a convex hexagon satisfying
,
,
, and
Let
,
, and
be the midpoints of
,
, and
. Prove that the circumcenter of
, the circumcenter of
, and the orthocenter of
are collinear.
Solution
We construct two equal triangles, prove that triangle is the medial triangle of both this triangles, use property of medial triangle and prove that circumcenters of constructed triangles coincide with given circumcenters.