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1988 Tournament Of Towns
(202) 6
TOT 202 1988 Autumn S6 S <=AM x CM + BM x DM, rectangle
TOT 202 1988 Autumn S6 S <=AM x CM + BM x DM, rectangle
Source:
March 7, 2021
geometry
rectangle
geometric inequality
Problem Statement
M
M
M
is an interior point of a rectangle
A
B
C
D
ABCD
A
BC
D
and
S
S
S
is its area. Prove that
S
≤
A
M
⋅
C
M
+
B
M
⋅
D
M
S \le AM \cdot CM + BM \cdot DM
S
≤
A
M
⋅
CM
+
BM
⋅
D
M
.(I.J . Goldsheyd)
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