Question Number 9627 by ridwan balatif last updated on 21/Dec/16
Commented by ridwan balatif last updated on 21/Dec/16
Commented by sou1618 last updated on 22/Dec/16
$$\bigtriangleup{ADE}\backsim\bigtriangleup{CME} \\ $$$${so} \\ $$$${AE}:{CE}={AD}:{CM} \\ $$$$\:\:{AE}:\left({AC}−{AE}\right)=\mathrm{2}:\mathrm{1} \\ $$$$\:\:{AE}=\mathrm{2}\left({AC}−{AE}\right) \\ $$$$\:\:{AE}=\frac{\mathrm{2}}{\mathrm{3}}{AC} \\ $$$$\:\:{AE}=\mathrm{52}\:. \\ $$$$ \\ $$
Answered by mrW last updated on 21/Dec/16
$$\frac{\mathrm{AE}}{\mathrm{EC}}=\frac{\mathrm{AD}}{\mathrm{MC}}=\frac{\mathrm{2}}{\mathrm{1}} \\ $$$$\mathrm{AE}=\mathrm{2}×\mathrm{EC}=\mathrm{2}×\left(\mathrm{AC}−\mathrm{AE}\right)=\mathrm{2}×\mathrm{AC}−\mathrm{2}×\mathrm{AE} \\ $$$$\mathrm{3}×\mathrm{AE}=\mathrm{2}×\mathrm{AC} \\ $$$$\mathrm{AE}=\frac{\mathrm{2}}{\mathrm{3}}×\mathrm{AC}=\frac{\mathrm{2}}{\mathrm{3}}×\mathrm{78}=\mathrm{52} \\ $$
Commented by ridwan balatif last updated on 21/Dec/16
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:\mathrm{for}\:\mathrm{your}\:\mathrm{help} \\ $$