Doubt in an extended triangle question.

Question

Consider a triangle $ABC$. The sides $AB$ and $A$C are extended to points $D$ and $E$, respectively, such that $|AD| = 3|AB|$ and $|AE| = 3|AC|$.
One diagonal of quadrilateral $BDEC$ divides the other diagonal in what ratio?

I got the answer $1:3$ but assuming the triangle isosceles and taking $A(0,0),\, B(-1,-1)$, and $C(1,-1)$. But how to approach the question without assuming anything?

Answer 1

Let $O$ be the point of intersection of diagonals. Consider $\triangle ABC$ and $\triangle ADE$ they are similar (why?). So if you consider $BCO$ and $DEO$ they are similar too, so $OE/OB = DE/BC = 3$.