GAUSS7 2020 Problem 24

In the 10 by 10 grid of squares shown, point P can be at any of the 41 points of intersection of pairs of gridlines inside (and not on) \triangle F G H. For each possible location of P, exactly three triangles are formed: \triangle F P G, \triangle G P H, \triangle H P F. How many of these 123 triangles have an area that is exactly half of the area of \triangle F G H?

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Answer Choices
A. 5
B. 7
C. 3
D. 11
E. 9