Menu Close

I-incenter-AB-BE-CF-internal-bisectors-in-ABC-Prove-that-8-AI-DI-BI-EI-CI-FI-4R-r-




Question Number 172694 by Shrinava last updated on 30/Jun/22
I-incenter  AB , BE , CF-internal bisectors in △ABC  Prove that  8 ≤ ((AI)/(DI)) ∙ ((BI)/(EI)) ∙ ((CI)/(FI)) ≤ ((4R)/r)
$$\mathrm{I}-\mathrm{incenter} \\ $$$$\mathrm{AB}\:,\:\mathrm{BE}\:,\:\mathrm{CF}-\mathrm{internal}\:\mathrm{bisectors}\:\mathrm{in}\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{8}\:\leqslant\:\frac{\mathrm{AI}}{\mathrm{DI}}\:\centerdot\:\frac{\mathrm{BI}}{\mathrm{EI}}\:\centerdot\:\frac{\mathrm{CI}}{\mathrm{FI}}\:\leqslant\:\frac{\mathrm{4R}}{\mathrm{r}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *