DEFINITION

If P, Q, R, and S are distinct points, then
let (PQ&RS) denote the line through the
midpoint of line segment PQ and
perpendicular to line RS.

PROVE THE FOLLOWING

If A, B, C, and D are distinct points on a
circle, then (AB&CD), (AC&BD), and
(AD&CB) are concurrent.

Although the problem only mentions 3 of the 6 possible feet that can be formed, they appear to all me concurrent.

If you hold A,B,C in place and move D around the circle, the concurrent point appears to trace out a circle of half the radius of the original circle.

Posted by Jer on 2012-05-24 14:05:14