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Contests
National and Regional Contests
Austria Contests
Austrian MO National Competition
2017 Federal Competition For Advanced Students
2
2
Part of
2017 Federal Competition For Advanced Students
Problems
(1)
Regular Pentagon
Source: Austrian Mathematical Olympiad 2017
5/2/2018
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a regular pentagon with center
M
M
M
. A point
P
P
P
(different from
M
M
M
) is chosen on the line segment
M
D
MD
M
D
. The circumcircle of
A
B
P
ABP
A
BP
intersects the line segment
A
E
AE
A
E
in
A
A
A
and
Q
Q
Q
and the line through
P
P
P
perpendicular to
C
D
CD
C
D
in
P
P
P
and
R
R
R
. Prove that
A
R
AR
A
R
and
Q
R
QR
QR
have same length. proposed by Stephan Wagner
geometry