A maltitude (midpoint-altitude) of quadrilateral ABCD is the
line segment MF (where M is the midpoint of side AB and F is
the foot of the perpendicular from M to the line CD). The
other three maltitudes are defined similarly.
Prove that the maltitudes of a cyclic quadrilateral are
Let ABCD be a cyclic quadrilateral that is not a rectangle.
Let T be the point of concurrency of the maltitudes and
Z the intersection of the diagonals. Prove the follwing:
T = Z ⇔ AC ⊥ BD.
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