Track / Stage 5 / 104 of 400 #704 of 2000

Problem 704

AIME late

Geometry Difficulty 5.3 Prove it

23rd Easy Autumn 2001 Problem Junior 5 There is a set of at least 4 points in the plane. If any one of the points is removed, then the others have an axis of symmetry. Must the set of all the points have an axis of symmetry?

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

23rd Easy Autumn 2001 (C) John Scholes [email protected] 15 Aug 2002

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.