Question Number 204657 by es last updated on 24/Feb/24
$${Consider}\:{point}\:{A}\:{inside}\:{a}\:{triangle} \\ $$$${with}\:{sides}\:\mathrm{3},\mathrm{4}\:{and}\:\mathrm{5}.\:{if}\:{d}\:\:{is}\:{the}\:{sum} \\ $$$$\:{of}\:{the}\:{distances}\:\:{of}\:{this}\:{point}\:{from} \\ $$$${the}\:{sides}.{what}\:{is}\:{the}\:{smallest} \\ $$$${value}\:{of}\:{d}? \\ $$$$ \\ $$
Answered by mr W last updated on 24/Feb/24
$${d}_{{min}} =\frac{\mathrm{3}×\mathrm{4}}{\mathrm{5}}=\mathrm{2}.\mathrm{4} \\ $$$${d}_{{max}} =\frac{\mathrm{3}×\mathrm{4}}{\mathrm{3}}=\mathrm{4} \\ $$
Commented by mr W last updated on 25/Feb/24
$${generally}: \\ $$$${d}_{{min}} =\frac{\mathrm{2}\Delta}{{max}\left({a},{b},{c}\right)} \\ $$$${d}_{{max}} =\frac{\mathrm{2}\Delta}{{min}\left({a},{b},{c}\right)} \\ $$$${with}\:\Delta={area}\:{of}\:{triangle} \\ $$
Commented by mr W last updated on 26/Feb/24
