I am studying barycentric coordinate. How do you prove the Menelaus' theorem using barycentric coordinate.
My Attempt: Let $P,Q,R$ be points in $BC,CA,AB$ respectively $A= (1,0,0)$ $B=(0,1,0)$ $C = (0,0,1)$ $P=(0,p,1-p)$ $Q = (1-q,0,q)$ $R = (r,1-r,0)$ $\frac{BP}{PC} \cdot \frac{CQ}{AQ} \cdot \frac{AR}{RB} = 1 \iff pqr=(1-p)(1-q)(1-r)$ . I then used the area formula to determine the equation of $PR,RQ$. I don't know that to do next.