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Question Number 133679 by Ar Brandon last updated on 23/Feb/21

Commented by Ar Brandon last updated on 23/Feb/21

$$\mathrm{If}\mathrm{M}\mathrm{is}\mathrm{orthocenter},\mathrm{prove}\mathrm{that}$$$$\frac{\mathrm{Area}\left[\mathrm{ABC}\right]}{\mathrm{Area}\left[{\mathrm{A}}^{″}{\mathrm{B}}^{″}{\mathrm{C}}^{″}\right]}=\frac{1}{4}$$

Commented by mr W last updated on 23/Feb/21

$$inthediagramMisnotthe$$$$orthocenterof{A}^{″}{B}^{″}{C}^{″}.$$$$eventhoughMistheorthocenter,$$$$i{don}^{\prime }tthinkitisalwaystruethat$$$$\frac{\mathrm{\Delta }ABC}{\mathrm{\Delta }{A}^{″}{B}^{″}{C}^{″}}=\frac{1}{4}.forexample,whatif$$$$\mathrm{\Delta }{A}^{″}{B}^{″}{C}^{″}isarighttriangle.$$$$canyoupleaserecheckthequestion?$$

Commented by Ar Brandon last updated on 23/Feb/21

OK Sir

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