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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1993 Dutch Mathematical Olympiad
2
2
Part of
1993 Dutch Mathematical Olympiad
Problems
(1)
determine the ratio
Source: Netherlands 1993
6/28/2009
In a triangle
A
B
C
ABC
A
BC
with \angle A\equal{}90^{\circ},
D
D
D
is the midpoint of
B
C
BC
BC
,
F
F
F
that of
A
B
AB
A
B
,
E
E
E
that of
A
F
AF
A
F
and
G
G
G
that of
F
B
FB
FB
. Segment
A
D
AD
A
D
intersects
C
E
,
C
F
CE,CF
CE
,
CF
and
C
G
CG
CG
in
P
,
Q
P,Q
P
,
Q
and
R
R
R
, respectively. Determine the ratio:
P
Q
Q
R
\frac{PQ}{QR}
QR
PQ
.
ratio
geometry proposed
geometry