MEMO 2017 pojedinačno problem 3
Dodao/la: arhivaSept. 12, 2018
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 $P$.
Source: Srednjoeuropska matematička olimpijada 2017, pojedinačno natjecanje, problem 3