Question Number 177767 by mnjuly1970 last updated on 08/Oct/22
$$ \\ $$$$\:\:{in}\:{A}\overset{\Delta} {{B}C}\:{prove}\:{that}: \\ $$$$\:\:\:{r}_{{a}} \:+\:{r}_{\:{b}} \:+{r}_{\:{c}} \:=\:{r}\:+\mathrm{4}{R} \\ $$$$\:\:\:\:\:{r}_{\:{a}} \::\:{escribed}\:\:{circle}\:{radius} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{corresponding}\:{to}\:{A}. \\ $$$$\:\:\:\:{r}\::\:\:{incirle}\:{radius}\: \\ $$$$\:\:\:\:\:\:{R}:\:{circumcircle}\:{radius} \\ $$