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Austrian MO Beginners' Competition
2000 Austria Beginners' Competition
4
4
Part of
2000 Austria Beginners' Competition
Problems
(1)
AC \cap GE =circumcenter of AGP in half regular dodecagon ABCDEFG
Source: 2000 Austria Beginners' Competition p4
10/4/2022
Let
A
B
C
D
E
F
G
ABCDEFG
A
BC
D
EFG
be half of a regular dodecagon . Let
P
P
P
be the intersection of the lines
A
B
AB
A
B
and
G
F
GF
GF
, and let
Q
Q
Q
be the intersection of the lines
A
C
AC
A
C
and
G
E
GE
GE
. Prove that
Q
Q
Q
is the circumcenter of the triangle
A
G
P
AGP
A
GP
.
geometry
circumcircle
3D geometry
dodecahedron