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Swedish Mathematical Competition
1988 Swedish Mathematical Competition
1
1
Part of
1988 Swedish Mathematical Competition
Problems
(1)
a+h_a > b+h_b > c+h_c if a > b > c, and h_i their altitudes
Source: 1988 Swedish Mathematical Competition p1
3/28/2021
Let
a
>
b
>
c
a > b > c
a
>
b
>
c
be sides of a triangle and
h
a
,
h
b
,
h
c
h_a,h_b,h_c
h
a
,
h
b
,
h
c
be the corresponding altitudes. Prove that
a
+
h
a
>
b
+
h
b
>
c
+
h
c
a+h_a > b+h_b > c+h_c
a
+
h
a
>
b
+
h
b
>
c
+
h
c
.
geometry
altitudes
Geometric Inequalities