MathDB

Consider

\triangle MAB

with a right angle at

A

and circumcircle

\omega

. Take any chord

CD

perpendicular to

AB

such that

A, C, B, D, M

lie on

\omega

in this order. Let

AC

and

MD

intersect at point

E

, and let

O

be the circumcenter of

\triangle EMC

. Show that if

J

is the intersection of

BC

and

OM

, then

JB = JM

.
(Proposed by Matthew Kung Wei Sheng and Ivan Chan Kai Chin)

Problem Statement