MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2016
P3
Beautiful geometrical inequality
Beautiful geometrical inequality
Source: Russian TST 2016, Day 8 P3 (Group NG)
April 19, 2023
geometry
Inequality
Problem Statement
Prove that for any points
A
,
B
,
C
,
D
A,B,C,D
A
,
B
,
C
,
D
in the plane, the following inequality holds
A
B
D
A
+
D
B
+
B
C
D
B
+
D
C
⩾
A
C
D
A
+
D
C
.
\frac{AB}{DA+DB}+\frac{BC}{DB+DC}\geqslant\frac{AC}{DA+DC}.
D
A
+
D
B
A
B
+
D
B
+
D
C
BC
⩾
D
A
+
D
C
A
C
.
Back to Problems
View on AoPS