CAYLEY 2020 Problem 24

A cube with vertices F G H J K L M N has edge length 200 . Point P is on H G, as shown. The shortest distance from G to a point inside \triangle P F M is 100 . Which of the following is closest to the length of H P?

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Answer Choices
A. 53
B. 55
C. 57
D. 59
E. 61