VTMO 2021 — Grade 7 — vtmo Question 17

$M$ is inside equilateral $ABC$, with perpendicular feet $D , E , F$ on $BC , CA , AB$. $MD = 1 , ME = 2 , MF = 3$. $a$) Find area $ABC$. $b ) BH \perp AC$ at $H$ and $G$ lies on $BH$ with $BG = 2 GH$. Prove $GM \parallel AC$.