Number Theory Geometry

Geometry Level 4

A right-angled triangle, ABC, with integer-side lengths has right angle B. The angle bisector of B meets AC at F. The altitude (perpendicular) from A to BF meets BF at E. The midpoint of hypotenuse AC is M. Line ME meets AB at D.

If EM = 49, what is the minimum value of AB+BC+AC?

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