2015 IMO Problems/Problem 3
Let be an acute triangle with
. Let
be its circumcircle,
its orthocenter, and
the foot of the altitude from
. Let
be the midpoint of
. Let
be the point on
such that $\angleHKQ=90\degree$ (Error compiling LaTeX. Unknown error_msg). Assume that the points
,
,
,
, and
are all different, and lie on
in this order.
Prove that the circumcircles of triangles and
are tangent to each other.