MathDB

Given quadrilateral

ABCD

AC

and

BD

meets at

E

, and

M, N

are the midpoints of

AC, BD

, respectively. Let the circumcircles of

ABE

and

CDE

meets again at

X\neq E

. Prove that

E, M, N, X

are concyclic.
Proposed by chengbilly

G1