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APMO
2015 APMO
1
1
Part of
2015 APMO
Problems
(1)
APMO 2015 P1
Source: APMO 2015
3/30/2015
Let
A
B
C
ABC
A
BC
be a triangle, and let
D
D
D
be a point on side
B
C
BC
BC
. A line through
D
D
D
intersects side
A
B
AB
A
B
at
X
X
X
and ray
A
C
AC
A
C
at
Y
Y
Y
. The circumcircle of triangle
B
X
D
BXD
BX
D
intersects the circumcircle
ω
\omega
ω
of triangle
A
B
C
ABC
A
BC
again at point
Z
Z
Z
distinct from point
B
B
B
. The lines
Z
D
ZD
Z
D
and
Z
Y
ZY
Z
Y
intersect
ω
\omega
ω
again at
V
V
V
and
W
W
W
respectively. Prove that
A
B
=
V
W
AB = V W
A
B
=
VW
Proposed by Warut Suksompong, Thailand
geometry
APMO
circumcircle