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1985 IMO Longlists
39
Concurrency of three lines
Concurrency of three lines
Source:
September 13, 2010
trigonometry
geometry
trig identities
Law of Sines
geometry proposed
Problem Statement
Given a triangle
A
B
C
ABC
A
BC
and external points
X
,
Y
X, Y
X
,
Y
, and
Z
Z
Z
such that
∠
B
A
Z
=
∠
C
A
Y
,
∠
C
B
X
=
∠
A
B
Z
\angle BAZ = \angle CAY , \angle CBX = \angle ABZ
∠
B
A
Z
=
∠
C
A
Y
,
∠
CBX
=
∠
A
BZ
, and
∠
A
C
Y
=
∠
B
C
X
\angle ACY = \angle BCX
∠
A
C
Y
=
∠
BCX
, prove that
A
X
,
B
Y
AX,BY
A
X
,
B
Y
, and
C
Z
CZ
CZ
are concurrent.
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