Proofs problem

[Saad]

AB is the diameter of a semicircle. Points C and D are ANY two points on the arc of the semicircle. AD and BC intersect at E. AC and BD are extended to meet at F. Prove that FE extended is perpendicular to AB.

I need any help possible because i have no idea of how to solve this proof problem!! plzzzzzzzzzzzzzz

[arildno]

The assertion is fairly easy to prove if you rephrase it in the terms of analytical geometry.
It looks difficult to prove it by "classical" means (i.e. identifying congruent triangles and suchlike)

[HallsofIvy]

Use the fact that triangles ACB and ADB are right triangles with right angle at C and D.