MathDB

Let

ABC

a triangle and let

\omega

be its circumcircle. Let

E{}

be the midpoint of the minor arc

BC

\omega

, and

M{}

the midpoint of

BC

. Let

V

be the other point of intersection of

AM

with

\omega

F{}

the point of intersection of

AE

with

BC

X{}

the other point of intersection of the circumcircle of

FEM

with

\omega

X'

the reflection of

V{}

with respect to

M{}

A'{}

the foot of the perpendicular from

A{}

BC

and

S{}

the other point of intersection of

XA'

with

\omega

. If

Z \in \omega

with

Z\neq X

is such that

AX = AZ

, then prove that

S, X'

and

Z{}

are collinear.

Problem Statement