MathDB

Consider

\triangle ABC

. Choose a point

M

on side

BC

and let

O

be the center of the circle passing through the vertices of

\triangle ABM

. Let

k

be the circle that passes through

A

and

M

and whose center lies on

BC

. Let line

MO

intersect

K

again in point

K

. Prove that the line

BK

is the same for any point

M

on segment

BC

, so long as all of these constructions are well-defined.
Proposed by Evan Chen

Problem Statement