MathDB

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

C3