Joel's Problem 2

Geometry Level 4

ABC is an acute-angled triangle and DEF is a straight line such that D, E, F are on BC(extended), segments AB, AC respectively. BF and CE intersect at G, and H is on BC such that A, G, H are collinear.

Find the sum of all possible values of \[\frac {BH \cdot DC}{HC \cdot DB}\].

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