MathDB

Let

ABC

be a triangle with circumcircle

\Omega

and incentre

I

. Let the line passing through

I

and perpendicular to

CI

intersect the segment

BC

and the arc

BC

(not containing

A

) of

\Omega

at points

U

and

V

, respectively. Let the line passing through

U

and parallel to

AI

intersect

AV

X

, and let the line passing through

V

and parallel to

AI

intersect

AB

Y

. Let

W

and

Z

be the midpoints of

AX

and

BC

, respectively. Prove that if the points

I, X,

and

Y

are collinear, then the points

I, W ,

and

Z

are also collinear.
Proposed by David B. Rush, USA

Problem Statement