All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Collinear Intersections (Posted on 2007-09-13) Difficulty: 3 of 5
Three circles A, B, and C have non-collinear centers, unequal radii, and pairwise the distance between their centers is greater than the sum of their radii.

Let P, Q, and R be the intersections of the external tangents to circles A&B, A&C, and B&C respectively.

Let L and M be the intersections of the internal tangents to circles A&B and A&C respectively.

Prove that P, Q, and R are collinear.

Prove that L, M, and R are collinear.

See The Solution Submitted by Bractals    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Monge's Circle Theorem Comment 1 of 1

The first problem, prove P, Q, and R are colinear, is known as Monge's Circle Theorem.

http://mathworld.wolfram.com/MongesCircleTheorem.html


  Posted by Brian Smith on 2009-11-07 12:11:10
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information