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concyclic points wanted, parallels and circumcircle given

Source: Tuymaada Junior 2007 p7

May 12, 2019

geometrycircumcircleConcyclicparallel

Problem Statement

On the

AB

side of the triangle

ABC

, points

X

and

Y

are chosen, on the side of

AC

is a point of

Z

, and on the side of

BC

is a point of

T

. Wherein

XZ \parallel BC

YT \parallel AC

. Line

TZ

intersects the circumscribed circle of triangle

ABC

at points

D

and

E

. Prove that points

X

Y

D

and

E

lie on the same circle.