This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

2021 Iranian Geometry Olympiad, 3

Given a convex quadrilateral $ABCD$ with $AB = BC $and $\angle ABD = \angle BCD = 90$.Let point $E$ be the intersection of diagonals $AC$ and $BD$. Point $F$ lies on the side $AD$ such that $\frac{AF}{F D}=\frac{CE}{EA}$.. Circle $\omega$ with diameter $DF$ and the circumcircle of triangle $ABF$ intersect for the second time at point $K$. Point $L$ is the second intersection of $EF$ and $\omega$. Prove that the line $KL$ passes through the midpoint of $CE$. [i]Proposed by Mahdi Etesamifard and Amir Parsa Hosseini - Iran[/i]