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Contests
National and Regional Contests
Portugal Contests
Portugal MO
2007 Portugal MO
2
2
Part of
2007 Portugal MO
Problems
(1)
concurrent circumcircles wanted 2007 Portugal p2
Source:
10/13/2020
Let
[
A
B
C
]
[ABC]
[
A
BC
]
be a triangle and
X
,
Y
X, Y
X
,
Y
and
Z
Z
Z
points on the sides
[
A
B
]
,
[
B
C
]
[AB], [BC]
[
A
B
]
,
[
BC
]
and
[
A
C
]
[AC]
[
A
C
]
, respectively. Prove that circumcircles of triangles
A
X
Z
,
B
X
Y
AXZ, BXY
A
XZ
,
BX
Y
and
C
Y
Z
CYZ
C
Y
Z
intersect at a point.
geometry
circumcircle
concurrent
concurrency