The three Cevian's are concurrent at point T. Show that all six small triangles have equal areas.

Question

It is given that $\Delta ART$, $\Delta BPT$, and $\Delta CQT$ have an area of one. I have no idea how to approach showing that all of the triangles have an equal area of one.

I shaded the three equal areas green in my construction.

Answer 1

HINTS: $\frac{1+D}{1+E}=F$ and cyclic permutations give $DEF=1$ and $DE+EF+FD=3$.
Do you know the Arithmetic-Geometric Mean?