MathDB

JBMO Shortlist 2021 G4

Source: JBMO Shortlist 2021

July 2, 2022

JuniorBalkanshortlist2021geometryconcurrency

Problem Statement

Let

ABCD

be a convex quadrilateral with

\angle B = \angle D = 90^{\circ}

. Let

E

be the point of intersection of

BC

with

AD

and let

M

be the midpoint of

AE

. On the extension of

CD

, beyond the point

D

, we pick a point

Z

such that

MZ = \frac{AE}{2}

. Let

U

and

V

be the projections of

A

and

E

respectively on

BZ

. The circumcircle of the triangle

CI

meets again

AE

at the point

L

. If

I

is the point of intersection of

BZ

with

AE

, prove that the lines

BL

and

CI

intersect on the line

AZ

.

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