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With the limited information provided by the question, the only statement which must be true is FJ = JH.
Not enough information has been given but if a given line bisects another line at 90 degrees then it is the perpendicular bisector of that line.
The answer is a point, the other person is correct.
circumcenter
Oh, dude, geometry words that start with J? Like, who even uses geometry words that start with J? But hey, if you really wanna know, there's "juxtapose" where you just put things side by side, and "joint" where things come together. But seriously, who cares about geometry words that start with J?