Question 16
Let $M$ be a point inside equilateral triangle $ABC$. Let $D,E,F$ be the perpendicular projections of $M$ onto $BC,CA,AB$, respectively. Given $MD=1$, $ME=2$ and $MF=3$:
a) Find the area of triangle $ABC$.
b) The line through $B$ perpendicular to $AC$ meets $AC$ at $H$. On $BH$, choose $G$ so that $BG=2GH$. Prove that $GM\parallel AC$.
a) Find the area of triangle $ABC$.
b) The line through $B$ perpendicular to $AC$ meets $AC$ at $H$. On $BH$, choose $G$ so that $BG=2GH$. Prove that $GM\parallel AC$.