MathDB

Concurrency in a cyclic hexagon

Source: 2022 China TST, Test 1, P1 (posting for better LaTeX)

March 24, 2022

geometryhexagonconcurrency

Problem Statement

In a cyclic convex hexagon

ABCDEF

AB

and

DC

intersect at

G

AF

and

DE

intersect at

H

. Let

M, N

be the circumcenters of

BCG

and

EFH

, respectively. Prove that the

BE

CF

and

MN

are concurrent.