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Area of triangle from collinear points

2175ExpertCoordinate GeometryTriangles

AIME II

Six points $A$, $B$, $C$, $D$, $E$, and $F$ lie in a straight line in that order. Suppose that $G$ is a point not on the line and that $AC = 26$, $BD = 22$, $CE = 31$, $DF = 33$, $AF = 73$, $CG = 40$, and $DG = 30$. Find the area of $\triangle BGE$.
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