MathDB

Conex polygon is cyclic iff one can assign of real numbers

Source: IMO Shortlist 2000, G4

August 10, 2008

trigonometrygeometryCyclicpolygonIMO Shortlist

Problem Statement

Let

A_1A_2 \ldots A_n

be a convex polygon,

n \geq 4.

Prove that

A_1A_2 \ldots A_n

is cyclic if and only if to each vertex

A_j

one can assign a pair

(b_j, c_j)

of real numbers,

j = 1, 2, \ldots, n,

so that

A_iA_j = b_jc_i - b_ic_j

for all

i, j

with

1 \leq i < j \leq n.