MathDB

Let

ABCD

be a circumscribed quadrilateral (i. e. a quadrilateral which has an incircle). The exterior angle bisectors of the angles

DAB

and

ABC

intersect each other at

K

; the exterior angle bisectors of the angles

ABC

and

BCD

intersect each other at

L

; the exterior angle bisectors of the angles

BCD

and

CDA

intersect each other at

M

; the exterior angle bisectors of the angles

CDA

and

DAB

intersect each other at

N

. Let

K_{1}

L_{1}

M_{1}

and

N_{1}

be the orthocenters of the triangles

ABK

BCL

CDM

and

DAN

, respectively. Show that the quadrilateral

K_{1}L_{1}M_{1}N_{1}

is a parallelogram.

Problem Statement