In an equilateral triangle, the incentre, circumcentre, orthocentre and centroid are :

In the adjoining figure, $\mathrm{D}$ is the midpoint of $\mathrm{BC}$ of a $\mathrm{\Delta ABC}.\mathrm{DM}$ and $\mathrm{DN}$ are the perpendiculars on $\mathrm{AB}$ and $\mathrm{AC}$ respectively and $\mathrm{DM}=\mathrm{DN}$, then the $∆\mathrm{ABC}$ is :

In the adjoining figure of $∆\mathrm{ABC}$, $\mathrm{AD}$ is the perpendicular bisector of side $\mathrm{BC}$. The triangle $\mathrm{ABC}$ is:

In a $∆\mathrm{ABC},\mathrm{D}$ is the mid-point of $\mathrm{BC}$ and $\mathrm{E}$ is mid-point of $\mathrm{AD}, \mathrm{BF}$ passes through $\mathrm{E}$. What is the ratio of $\mathrm{AF}: \mathrm{FC} ?$