Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I need help with the following problem:

Given a triangle ABC. The external bisector of angle A intersects the line BC at point N. The internal bisector of angle A intersects BC at point M. Let k be the circle with diameter MN. Prove that for every point Q on the circle QB:QC=AB:AC.

Remark: The problem has to be solved using only the properties of the bisectors and Thales' theorem.

share|improve this question
    
I wouldn't be surprised if this is in C. Stanley Ogilvy's book Excursions in Geometry, where it treats harmonic division. Whether his proof satisfies the constraints in your "Remark" is another question. –  Michael Hardy Feb 21 '12 at 19:58
    
Why is it that the problem has to be solved using only those tools? Is it, by any chance, a homework problem? It's OK if it is, but if it is you should add the homework tag. –  Gerry Myerson Feb 21 '12 at 22:27
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.