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Baltic Way
1998 Baltic Way
11
11
Part of
1998 Baltic Way
Problems
(1)
9-th Baltic Way
Source:
9/29/2010
If
a
,
b
,
c
a,b,c
a
,
b
,
c
be the lengths of the sides of a triangle. Let
R
R
R
denote its circumradius. Prove that
R
≥
a
2
+
b
2
2
2
a
2
+
2
b
2
−
c
2
R\ge \frac{a^2+b^2}{2\sqrt{2a^2+2b^2-c^2}}
R
≥
2
2
a
2
+
2
b
2
−
c
2
a
2
+
b
2
When does equality hold?
trigonometry
inequalities
geometry
inequalities proposed