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Contests
International Contests
Nordic
2019 Nordic
2
Geometric inequality
Geometric inequality
Source: Nordic 2019, P2
April 7, 2019
inequalities
geometric inequality
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be the side lengths of a right angled triangle with c > a, b. Show that
3
<
c
3
−
a
3
−
b
3
c
(
c
−
a
)
(
c
−
b
)
≤
2
+
2.
3<\frac{c^3-a^3-b^3}{c(c-a)(c-b)}\leq \sqrt{2}+2.
3
<
c
(
c
−
a
)
(
c
−
b
)
c
3
−
a
3
−
b
3
≤
2
+
2.
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