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If-a-circle-of-radius-r-is-inscribed-in-a-triangl-ABC-Express-r-in-terms-of-a-b-and-c-only-




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
$${If}\:{a}\:{circle}\:{of}\:{radius}\:{r}\:{is}\:{inscribed}\:{in} \\ $$$${a}\:{triangl}\:{ABC}.\:{Express}\:{r}\:{in}\:{terms}\:{of} \\ $$$${a},{b}\:{and}\:{c}\:{only} \\ $$
Answered by AST last updated on 18/Dec/23
r=((√(s(s−a)(s−b)(s−c)))/s) where s=((a+b+c)/2)
$${r}=\frac{\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}}{{s}}\:{where}\:{s}=\frac{{a}+{b}+{c}}{\mathrm{2}} \\ $$
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 AST last updated on 18/Dec/23
rs=area of the triangle=(√(s(s−a)(s−b)(s−c)))
$${rs}={area}\:{of}\:{the}\:{triangle}=\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)} \\ $$
Commented by necx122 last updated on 18/Dec/23
Thanks

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