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Czech-Polish-Slovak Match
2022 Czech-Austrian-Polish-Slovak Match
5
5
Part of
2022 Czech-Austrian-Polish-Slovak Match
Problems
(1)
Geo with angle bisector
Source: Czech-Polish-Slovak Match 2022 P5
9/3/2022
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
<
A
C
AB < AC
A
B
<
A
C
and circumcenter
O
O
O
. The angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
meets the side
B
C
BC
BC
at
D
D
D
. The line through
D
D
D
perpendicular to
B
C
BC
BC
meets the segment
A
O
AO
A
O
at
X
X
X
. Furthermore, let
Y
Y
Y
be the midpoint of segment
A
D
AD
A
D
. Prove that points
B
,
C
,
X
,
Y
B, C, X, Y
B
,
C
,
X
,
Y
are concyclic.
geometry
angle bisector