DEFINITION

If X is a point not on line YZ, then
the foot of the perpendicular from X
to YZ is the point X' on YZ such that
XX' ⊥ YZ.

PROVE THE FOLLOWING

If A, B, C, and D are distinct points
on a circle such that lines AB and CD
are not perpendicular, then the feet
of the perpendiculars from A and B to
to CD and the feet of the perpendiculars
from C and D to AB lie on a circle.