Let A', B', C', and D' be the feet of points
A, B, C, and D respectively. If lines AB and
CD are parallel, then the the feet form the
vertices of an isosceles trapezoid ( a rect-
angle if |AB| = |CD ) and therefore lie on a
circle; otherwise, let O be the point of
intersection and θ the minimum of ∠AOC
and ∠AOD. Then
|OA||OB| = |OC||OD|
==> |OA|cos(θ|OB|cos(θ) =
|OC|cos(θ|OD|cos(θ)
==> |OA'||OB'| = |OC'||OD'|
==> A', B', C', and D' lie on a circle.
QED
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