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National and Regional Contests
Argentina Contests
Argentina National Olympiad
1995 Argentina National Olympiad
3
3
Part of
1995 Argentina National Olympiad
Problems
(1)
Parallelogram
Source: Argentinian National Olympiad- 1995-level 3
8/10/2018
Let ABCD be a parallelogram, and P a point such that
2
P
D
A
=
A
B
P
2 PDA=ABP
2
P
D
A
=
A
BP
and
2
P
A
D
=
P
C
D
2 PAD=PCD
2
P
A
D
=
PC
D
Show that
A
B
=
B
P
=
C
P
AB=BP=CP
A
B
=
BP
=
CP
geometry
parallelogram