Question Number 171688 by Shrinava last updated on 20/Jun/22
![In △ABC AA^′ , BB^′ , CC^′ - cevians AA^′ ∩ BB^′ ∩ CC^′ = {P} Prove that: min([APC^′ ],[BPA^′ ],[CPB^′ ])+min([APB^′ ],[BPC^′ ],[CPA^′ ]) ≤ ((Rr (√3))/2)](Q171688.png)
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{AA}^{'} \:,\:\mathrm{BB}^{'} \:,\:\mathrm{CC}^{'} \:-\:\mathrm{cevians} \\ $$$$\mathrm{AA}^{'} \:\cap\:\mathrm{BB}^{'} \:\cap\:\mathrm{CC}^{'} \:=\:\left\{\mathrm{P}\right\} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{min}\left(\left[\mathrm{APC}^{'} \right],\left[\mathrm{BPA}^{'} \right],\left[\mathrm{CPB}^{'} \right]\right)+\mathrm{min}\left(\left[\mathrm{APB}^{'} \right],\left[\mathrm{BPC}^{'} \right],\left[\mathrm{CPA}^{'} \right]\right)\:\leqslant\:\frac{\mathrm{Rr}\:\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$