Math
posted by Kole .
Let A, C be the endpoints of the diameter of a circle and B an arbitrary point on the circle. Using the
slopes of secant lines show that \ABC is a right angle. You can assume the circle is centered at the
origin.

we can without loss of generality assume the radius is 1, and the diameter is on the xaxis. the coordinates of B are (cosθ,sinθ).
slope of AB = sinθ/(1+cosθ)
slope of CB = sinθ/(1cosθ)
product of slopes: sin^2 θ/(1cos^2 θ) = 1
so, the lines are perpendicular. 
Steve your a boss for asking this question, you just saved me 2 hours of my life trying to figure it out, YEEEE

Kole*