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Czech-Polish-Slovak Match
2019 Czech-Austrian-Polish-Slovak Match
1
1
Part of
2019 Czech-Austrian-Polish-Slovak Match
Problems
(1)
Prove B,E,F,Y cyclic
Source: Czech-Polish-Slovak Match 2019 P1
7/15/2019
Let
ω
\omega
ω
be a circle. Points
A
,
B
,
C
,
X
,
D
,
Y
A,B,C,X,D,Y
A
,
B
,
C
,
X
,
D
,
Y
lie on
ω
\omega
ω
in this order such that
B
D
BD
B
D
is its diameter and
D
X
=
D
Y
=
D
P
DX=DY=DP
D
X
=
D
Y
=
D
P
, where
P
P
P
is the intersection of
A
C
AC
A
C
and
B
D
BD
B
D
. Denote by
E
,
F
E,F
E
,
F
the intersections of line
X
P
XP
XP
with lines
A
B
,
B
C
AB,BC
A
B
,
BC
, respectively. Prove that points
B
,
E
,
F
,
Y
B,E,F,Y
B
,
E
,
F
,
Y
lie on a single circle.
geometry