In-ABC-AA-BB-CC-cevians-AA-BB-CC-P-Prove-that-min-APC-BPA-CPB-min-APB-BPC-CPA-Rr-3-2-

Question Number 171688 by Shrinava last updated on 20/Jun/22

In △ ABC

{AA}^{^{'}}, {BB}^{^{'}}, {CC}^{^{'}} - cevians

{AA}^{^{'}} \cap {BB}^{^{'}} \cap {CC}^{^{'}} = {P}

Prove that :

\min ([{APC}^{^{'}}], [{BPA}^{^{'}}], [{CPB}^{^{'}}]) + \min ([{APB}^{^{'}}], [{BPC}^{^{'}}], [{CPA}^{^{'}}]) ⩽ \frac{Rr \sqrt{3}}{2}