Question Number 133679 by Ar Brandon last updated on 23/Feb/21
Commented by Ar Brandon last updated on 23/Feb/21
![If M is orthocenter, prove that ((Area[ABC])/(Area[A′′B′′C′′]))=(1/4)](Q133680.png)
$$\mathrm{If}\:\mathrm{M}\:\mathrm{is}\:\mathrm{orthocenter},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{Area}\left[\mathrm{ABC}\right]}{\mathrm{Area}\left[\mathrm{A}''\mathrm{B}''\mathrm{C}''\right]}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$
Commented by mr W last updated on 23/Feb/21
$${in}\:{the}\:{diagram}\:{M}\:{is}\:{not}\:{the} \\ $$$${orthocenter}\:{of}\:{A}''{B}''{C}''. \\ $$$${even}\:{though}\:{M}\:{is}\:{the}\:{orthocenter}, \\ $$$${i}\:{don}'{t}\:{think}\:{it}\:{is}\:{always}\:{true}\:{that} \\ $$$$\frac{\Delta{ABC}}{\Delta{A}''{B}''{C}''}=\frac{\mathrm{1}}{\mathrm{4}}.\:{for}\:{example},\:{what}\:{if} \\ $$$$\Delta{A}''{B}''{C}''\:{is}\:{a}\:{right}\:{triangle}. \\ $$$${can}\:{you}\:{please}\:{recheck}\:{the}\:{question}? \\ $$
Commented by Ar Brandon last updated on 23/Feb/21
OK Sir