MathDB

Socialists Republic Of Czechoslovakia 5

Source: IMO LongList 1959-1966 Problem 28

September 2, 2004

geometrycircleLocusLocus problemsIMO LonglistIMO Shortlist

Problem Statement

In the plane, consider a circle with center

S

and radius

1.

Let

ABC

be an arbitrary triangle having this circle as its incircle, and assume that

SA\leq SB\leq SC.

Find the locus of a.) all vertices

A

of such triangles; b.) all vertices

B

of such triangles; c.) all vertices

C

of such triangles.