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

Home > Shapes > Geometry
Equal Angles (Posted on 2005-12-14) Difficulty: 3 of 5
Let circle A be in the interior of circle B and tangent to it at point M. Let chord QR of circle B be tangent to circle A at point P. Prove that angles PMQ and PMR are equal.

1993 British Mathematical Olympiad,Round 1,Problem 4.

See The Solution Submitted by Bractals    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Question re: Is there an easier way? ??? | Comment 2 of 4 |
(In reply to Is there an easier way? by DrBob)

>Construct MN perpendicular to the tangent at M - this passes >through the centre of both circles. Call the centre of A, O

Why call the certre of A, O?  The center of A is A.

Where exactly is N?  Is MN a diameter of circle A?  If so that would make angle MPN = 90 but it would certainly not be true that angle NMR = angle NPR



  Posted by Jer on 2005-12-14 14:28:39
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information