MathDB

JBMO Shortlist 2022 G1

Source: JBMO Shortlist 2022

June 26, 2023

geometrypentagonCyclicJuniorBalkanshortlisttangent

Problem Statement

Let

ABCDE

be a cyclic pentagon such that

BC = DE

and

AB

is parallel to

DE

. Let

X, Y,

and

Z

be the midpoints of

BD, CE,

and

AE

respectively. Show that

AE

is tangent to the circumcircle of the triangle

XYZ

.
Proposed by Nikola Velov, Macedonia