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Canada National Olympiad
2017 Canada National Olympiad
4
4
Part of
2017 Canada National Olympiad
Problems
(1)
CMO 2017 P4
Source: Canadian Mathematical Olympiad 2017
3/31/2017
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram. Points
P
P
P
and
Q
Q
Q
lie inside
A
B
C
D
ABCD
A
BC
D
such that
△
A
B
P
\bigtriangleup ABP
△
A
BP
and
△
B
C
Q
\bigtriangleup{BCQ}
△
BCQ
are equilateral. Prove that the intersection of the line through
P
P
P
perpendicular to
P
D
PD
P
D
and the line through
Q
Q
Q
perpendicular to
D
Q
DQ
D
Q
lies on the altitude from
B
B
B
in
△
A
B
C
\bigtriangleup{ABC}
△
A
BC
.
geometry
parallelogram