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National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2018 JBMO TST-Turkey
6
6
Part of
2018 JBMO TST-Turkey
Problems
(1)
concyclic circumcenters, starting with a point that sees in equal angles in a #
Source: Turkey JBMO TST 2018 p6
9/16/2018
A point
E
E
E
is located inside a parallelogram
A
B
C
D
ABCD
A
BC
D
such that
∠
B
A
E
=
∠
B
C
E
\angle BAE = \angle BCE
∠
B
A
E
=
∠
BCE
. The centers of the circumcircles of the triangles
A
B
E
,
E
C
B
,
C
D
E
ABE,ECB, CDE
A
BE
,
ECB
,
C
D
E
and
D
A
E
DAE
D
A
E
are concyclic.
geometry
parallelogram
circumcircle
Concyclic
equal angles