Article View: rec.puzzles
Article #2689Re: Two Circles Puzzle
From: byron elbows / Brian Tung
Date: Wed, 27 Jan 1993 21:06
Date: Wed, 27 Jan 1993 21:06
18 lines
1451 bytes
1451 bytes
I wrote: > Q. Three circles of any radii r1, r2, and r3 can be drawn so that they > are mutually tangent. Also, a fourth circle can be drawn that is > tangent to the first three circles, but its radius is determined > by those of the other circles. If the circles are "close enough" > in radius, then the fourth circle surrounds the first three; > otherwise, it is external to the first three. Prove or disprove: > in those cases where the fourth circle surrounds the other three, > those three circles consume the maximum fraction of the area of > the fourth circle when r1=r2=r3. I should add that in all cases, TWO fourth circles can be drawn. One is always inside the first three. The other one is either external to the first three, or else it encloses the first three. byron elbows (mail to brian@cs.ucla.edu)
Technical Details
Message-ID:
<1993Jan27.210635.944@cs.ucla.edu>Path:
arc1-ca.pugleaf.net!sparky!uunet!math.fu-berlin.de!ira.uka.de!scsing.switch.ch!univ-lyon1.fr!ghost.dsi.unimi.it!rpi!usc!ucla-cs!maui.cs.ucla.edu!brianReferences:
<C1IyDB.2K5@fastrac.llnl.gov> <1993Jan27.202454.29728@cs.ucla.edu>Show Full Headers
Complete Article Headers
Newsgroups: rec.puzzles Path: arc1-ca.pugleaf.net!sparky!uunet!math.fu-berlin.de!ira.uka.de!scsing.switch.ch!univ-lyon1.fr!ghost.dsi.unimi.it!rpi!usc!ucla-cs!maui.cs.ucla.edu!brian From: brian@maui.cs.ucla.edu (byron elbows / Brian Tung) Subject: Re: Two Circles Puzzle Message-ID: <1993Jan27.210635.944@cs.ucla.edu> Keywords: geometry Sender: usenet@cs.ucla.edu (Mr Usenet) Nntp-Posting-Host: maui.cs.ucla.edu Organization: UCLA, Computer Science Department References: <C1IyDB.2K5@fastrac.llnl.gov> <1993Jan27.202454.29728@cs.ucla.edu> Date: Wed, 27 Jan 93 21:06:35 GMT Lines: 18