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Swedish Mathematical Competition
1981 Swedish Mathematical Competition
5
5
Part of
1981 Swedish Mathematical Competition
Problems
(1)
area inequality (XYZ) >= (AYZ), (BZX), (CXY)
Source: 1981 Swedish Mathematical Competition p5
3/28/2021
A
B
C
ABC
A
BC
is a triangle.
X
X
X
,
Y
Y
Y
,
Z
Z
Z
lie on
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
respectively. Show that area
X
Y
Z
XYZ
X
Y
Z
cannot be smaller than each of area
A
Y
Z
AYZ
A
Y
Z
, area
B
Z
X
BZX
BZX
, area
C
X
Y
CXY
CX
Y
.
geometry
Geometric Inequalities
areas