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National and Regional Contests
Hungary Contests
Kürschák Math Competition
1981 Kurschak Competition
1
1
Part of
1981 Kurschak Competition
Problems
(1)
AB + PQ + QR + RP <= AP + AQ + AR + BP + BQ + BR
Source: 1981 Hungary - Kürschák Competition p1
10/10/2022
Prove that
A
B
+
P
Q
+
Q
R
+
R
P
≤
A
P
+
A
Q
+
A
R
+
B
P
+
B
Q
+
B
R
AB + PQ + QR + RP \le AP + AQ + AR + BP + BQ + BR
A
B
+
PQ
+
QR
+
RP
≤
A
P
+
A
Q
+
A
R
+
BP
+
BQ
+
BR
where
A
,
B
,
P
,
Q
A, B, P, Q
A
,
B
,
P
,
Q
and
R
R
R
are any five points in a plane.
geometry
Geometric Inequalities