MathDB
Construct distance sqrt 2021

Source: CMO 2022 P5

December 22, 2021
geometry

Problem Statement

On a blank piece of paper, two points with distance 11 is given. Prove that one can use (only) straightedge and compass to construct on this paper a straight line, and two points on it whose distance is 2021\sqrt{2021} such that, in the process of constructing it, the total number of circles or straight lines drawn is at most 10.10. Remark: Explicit steps of the construction should be given. Label the circles and straight lines in the order that they appear. Partial credit may be awarded depending on the total number of circles/lines.