MathDB

points on a circle (Slovenia National MO 2001 4th Grade P4)

Source:

April 7, 2021

geometry

Problem Statement

Let

n\ge4

points on a circle be denoted by

1

through

n

. A pair of two nonadjacent points denoted by

a

and

b

is called regular if all numbers on one of the arcs determined by

a

and

b

are less than

a

and

b

. Prove that there are exactly

n-3

regular pairs.