MathDB

Cyclic Pentagon with Orthocenters

Source: 2019 China TST Test 1 Day 1 Q1

March 17, 2019

geometrycircumcircle

Problem Statement

ABCDE

is a cyclic pentagon, with circumcentre

O

.

AB=AE=CD

.

I

midpoint of

BC

.

J

midpoint of

DE

.

F

is the orthocentre of

\triangle ABE

, and

G

the centroid of

\triangle AIJ

.

CE

intersects

BD

at

H

,

OG

intersects

FH

at

M

. Show that

AM\perp CD

.

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