2018 USAMO Problems/Problem 5
Problem 5
In convex cyclic quadrilateral we know that lines
and
intersect at
lines
and
intersect at
and lines
and
intersect at
Suppose that the circumcircle of
intersects line
at
and
, and the circumcircle of
intersects line
at
and
, where
and
are collinear in that order. Prove that if lines
and
intersect at
, then