2019 IMO Problems/Problem 6
Problem
Let 
be the incenter of acute triangle 
with 
. The incircle ω of is tangent to sides 
, 
, and 
at 
, 
, and 
, respectively. The line through perpendicular to 
meets ω again at 
. Line 
meets ω again at 
. The circumcircles of triangles 
and 
meet again at 
.
Prove that lines 
and 
meet on the line through 
perpendicular to 
.
