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Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
9.5
9.5
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Cute angle chasing problem
Source: Sharygin Finals 2022 9.5
8/1/2022
Chords
A
B
AB
A
B
and
C
D
CD
C
D
of a circle
ω
\omega
ω
meet at point
E
E
E
in such a way that
A
D
=
A
E
=
E
B
AD = AE = EB
A
D
=
A
E
=
EB
. Let
F
F
F
be a point of segment
C
E
CE
CE
such that
E
D
=
C
F
ED = CF
E
D
=
CF
. The bisector of angle
A
F
C
AFC
A
FC
meets an arc
D
A
C
DAC
D
A
C
at point
P
P
P
. Prove that
A
A
A
,
E
E
E
,
F
F
F
, and
P
P
P
are concyclic.
geometry