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National and Regional Contests
Korea Contests
Korea National Olympiad
1997 Korea National Olympiad
7
7
Part of
1997 Korea National Olympiad
Problems
(1)
Jacobi wasn't well known back in 1997
Source: 1997 Korea National Olympiad #7
3/18/2018
Let
X
,
Y
,
Z
X,Y,Z
X
,
Y
,
Z
be the points outside the
△
A
B
C
\triangle ABC
△
A
BC
such that
∠
B
A
Z
=
∠
C
A
Y
,
∠
C
B
X
=
∠
A
B
Z
,
∠
A
C
Y
=
∠
B
C
X
.
\angle BAZ=\angle CAY,\angle CBX=\angle ABZ,\angle ACY=\angle BCX.
∠
B
A
Z
=
∠
C
A
Y
,
∠
CBX
=
∠
A
BZ
,
∠
A
C
Y
=
∠
BCX
.
Prove that the lines
A
X
,
B
Y
,
C
Z
AX, BY, CZ
A
X
,
B
Y
,
CZ
are concurrent.
geometry