MathDB

Let

AXYZB

be a convex pentagon inscribed in a semicircle with diameter

AB

, and let

K

be the foot of the altitude from

Y

AB

. Let

O

denote the midpoint of

AB

and

L

be the intersection of

XZ

with

YO

. Select a point

M

on line

KL

with

MA=MB

, and finally, let

I

be the reflection of

O

across

XZ

. Prove that if quadrilateral

XKOZ

is cyclic then so is quadrilateral

YOMI

.
Proposed by Evan Chen

Problem Statement