Track / Stage 5 / 3 of 400 #603 of 1964

Problem 603

AIME late

Geometry Difficulty 5.0 Prove it

Can three circles have one common point? two common points? three common points? four common points?

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

321. The answers to the first two questions are positive, to the third one - negative. (Provide an explanation.)

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.