Let be a convex pentagon. Let be the intersection of the lines and . Assume that and . Prove that the circumcentres of the triangles and are collinear with .
Let $ABCDE$ be a convex pentagon. Let $P$ be the intersection of the lines $CE$ and $BD$. Assume that $\angle PAD = \angle ACB$ and $\angle CAP = \angle EDA$. \\Prove that the circumcentres of the triangles $ABC$ and $ADE$ are collinear with $P$.
Izvor: Srednjoeuropska matematička olimpijada 2017, pojedinačno natjecanje, problem 3
Školjka 
be a convex pentagon. Let 
be the intersection of the lines 
and 
. Assume that 
and 
. 
and 
are collinear with