MathDB

Romania District Olympiad 2002 - Grade XI

Source:

March 18, 2011

trigonometrygeometry proposedgeometry

Problem Statement

In the

xOy

system, consider the points

A_n(n,n^3)

with

n\in \mathbb{N}^*

and the point

B(0,1)

. Prove that
a) for any positive integers

k>j>i\ge 1

, the points

A_i,A_j,A_k

cannot be collinear. b) for any positive integers

i_k>i_{k-1}>\ldots>i_1\ge 1

, we have

\mu(\widehat{A_{i_1}OB})+\mu(\widehat{A_{i_2}OB})+\cdots+\mu(\widehat{A_{i_k}OB})<\frac{\pi}{2}

***

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