Problem

Source:

Tags: Comc, 2018 COMC



Source: 2018 Canadian Open Math Challenge Part C Problem 3 Consider a convex quadrilateral $ABCD$. Let rays $BA$ and $CD$ intersect at $E$, rays $DA$ and $CB$ intersect at $F$, and the diagonals $AC$ and $BD$ intersect at $G$. It is given that the triangles $DBF$ and $DBE$ have the same area. $\text{(a)}$ Prove that $EF$ and $BD$ are parallel. $\text{(b)}$ Prove that $G$ is the midpoint of $BD$. $\text{(c)}$ Given that the area of triangle $ABD$ is 4 and the area of triangle $CBD$ is 6, (C.)compute the area of triangle $EFG$.