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 am not sure if the following result is well known. I stumbled across it from the paper The Perimetric Bisection of Triangles by Dov Avishalom, where the result was stated without proof. I am looking for a simple proof of the following

The following figure depicts a circular arc with chord $\mathrm{LN}$. The point $\mathrm{P}$ denotes the midpoint of the circular arc. We drop perpendicular from $\mathrm{P}$ to $\mathrm{LM}$, intersecting it at point $\mathrm{Q}$.

Then the claim is that $\mathrm{Q}$ bisects the broken line segment $\mathrm{LMN}$, that is we have $\mathrm{LQ} = \mathrm{QM}+\mathrm{MN}$.

circular arc

Thanks for any help.

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

This is the famous Broken Chord Theorem that goes back to Archimedes. With the right name to search for, you will easily find proofs.

share|improve this answer
    
Ah, so it is a well known result. Thank you André. –  EuYu Sep 16 '12 at 5:44
add comment

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.