AIR MATH

Math Question

In the diagram, which must be true for point D to be an orthocenter? \( \overline{\mathrm{BE}}, \overline{\mathrm{CF}} \), and \( \overline{\mathrm{AG}} \) are angle bisectors. \( \overline{\mathrm{BE}} \perp \overline{\mathrm{AC}}, \overline{\mathrm{AG}} \perp \overline{\mathrm{BC}} \), and \( \overline{\mathrm{CF}} \perp \overline{\mathrm{AB}} \). \( \overline{\mathrm{BE}} \) bisects \( \overline{\mathrm{AC}}, \overline{\mathrm{CF}} \) bisects \( \overline{\mathrm{AB}} \), and \( \overline{\mathrm{AG}} \) bisects \( \overline{\mathrm{BC}} \). \( \overline{\mathrm{BE}} \) is a perpendicular bisector of \( \overline{\mathrm{AC}}, \overline{\mathrm{CF}} \) is a perpendicular bisector of \( \overline{\mathrm{AB}} \), and \( \overline{\mathrm{AG}} \) is a perpendicular bisector of \( \overline{\mathrm{BC}} \).

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