8
$\begingroup$

enter image description here

Barrow's inequality states that if $P$ is any point inside triangle $ABC$, and $PU$, $PW$, and $PV$ are the angle bisectors, then the following inequality holds, $PA+PB+PC\geq 2(PU+PV+PW)$.

I know that it is a stronger version of the Erdos-Mordell inequality, of which some very short and elegant proofs have been found. However, I have not been able to find any proof of the Barrow's inequality on the internet. Can anyone give me the proof?

$\endgroup$
5
$\begingroup$

You can find a proof in Topics in Inequalities - Theorems and Techniques by Hojoo Lee. See e.g. here, Theorem 1.3.2.

$\endgroup$
  • $\begingroup$ Oh, thanks! ${}$ $\endgroup$ – Sawarnik Mar 30 '14 at 20:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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