compass and ruler
Source: All-Russian olympiad 1995, Grade 11, First Day, Problem 3
October 20, 2013
geometry proposedgeometry
Problem Statement
Two points on the distance 1 are given in a plane. It is allowed to draw a line through two marked points, as well as a circle centered in a marked point with radius equal to the distance between some two marked points. By marked points we mean the two initial points and intersection points of two lines, two circles, or a line and a circle constructed so far. Let be the minimum number of circles needed to construct two points on the distance if only a compass is used, and let be the minimum total number of circles and lines needed to do so if a ruler and a compass are used, where is a natural
number. Prove that the sequence is not bounded.
A. Belov