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1969 All Soviet Union Mathematical Olympiad
127
ASU 127All Soviet Union MO 1969 (n + 1)h_{n+1} - nh_n > R, apothem
ASU 127All Soviet Union MO 1969 (n + 1)h_{n+1} - nh_n > R, apothem
Source:
June 23, 2019
geometry
geometric inequality
Problem Statement
Let
h
k
h_k
h
k
be an apothem of the regular
k
k
k
-gon inscribed into a circle with radius
R
R
R
. Prove that
(
n
+
1
)
h
n
+
1
−
n
h
n
>
R
(n + 1)h_{n+1} - nh_n > R
(
n
+
1
)
h
n
+
1
−
n
h
n
>
R
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