Question Number 202001 by necx122 last updated on 18/Dec/23
$${If}\:{a}\:{circle}\:{of}\:{radius}\:{r}\:{is}\:{inscribed}\:{in} \\ $$$${a}\:{triangl}\:{ABC}.\:{Express}\:{r}\:{in}\:{terms}\:{of} \\ $$$${a},{b}\:{and}\:{c}\:{only} \\ $$
Answered by deleteduser1 last updated on 18/Dec/23
$${r}=\frac{\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}}{{s}}\:{where}\:{s}=\frac{{a}+{b}+{c}}{\mathrm{2}} \\ $$
Commented by necx122 last updated on 18/Dec/23
Thank you. Sir, I'm interested in the proof. If I can get that I'll be more grateful.
Commented by deleteduser1 last updated on 18/Dec/23
$${rs}={area}\:{of}\:{the}\:{triangle}=\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)} \\ $$
Commented by necx122 last updated on 18/Dec/23
Thanks