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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
One geometry term that starts with the letter "J" is "juxtaposition," which refers to the placement of two or more geometric shapes or figures next to each other. Another term is "joint," which is the point where two or more line segments meet. "Jacobian" is a term used in calculus and geometry to refer to the determinant of the Jacobian matrix, which represents how a change in variables affects the orientation of a geometric shape.