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Paraguay Contests
Paraguay Mathematical Olympiad
2007 Paraguay Mathematical Olympiad
3
3
Part of
2007 Paraguay Mathematical Olympiad
Problems
(1)
Paraguayan National Olympiad 2007, Level 3, Problem 3
Source:
9/1/2014
Let
A
B
C
D
ABCD
A
BC
D
be a square,
E
E
E
and
F
F
F
midpoints of
A
B
AB
A
B
and
A
D
AD
A
D
respectively, and
P
P
P
the intersection of
C
F
CF
CF
and
D
E
DE
D
E
. a) Show that
D
E
⊥
C
F
DE \perp CF
D
E
⊥
CF
. b) Determine the ratio
C
F
:
P
C
:
E
P
CF : PC : EP
CF
:
PC
:
EP
ratio
analytic geometry
graphing lines
slope