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Miklós Schweitzer
1958 Miklós Schweitzer
4
4
Part of
1958 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1958- Problem 4
Source:
10/21/2015
4. Let
P
1
P
2
P
3
P
4
P
5
P
6
P_1 P_2 P_3 P_4 P_5 P_6
P
1
P
2
P
3
P
4
P
5
P
6
be a convex hexagon. Denote by
T
T
T
its area and by
t
t
t
the area of the triangle
Q
1
Q
2
Q
3
Q_1 Q_2 Q_3
Q
1
Q
2
Q
3
, where
Q
1
,
Q
2
Q_1,Q_2
Q
1
,
Q
2
and
Q
3
Q_3
Q
3
are the midpoints of
P
1
P
4
,
P
2
P
5
,
P
3
P
6
P_1P_4,P_2P_5,P_3P_6
P
1
P
4
,
P
2
P
5
,
P
3
P
6
respectively. Prove that
t
<
1
4
T
t<\frac{1}{4}T
t
<
4
1
T
. (G. 3)
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