Investigation: Construct a circle. Construct four points on this circle and label them A, B, C and D. Construct segments AC and BD such that these segments intersect. Label the point of intersection E. A special relationship exists between segments AE, BE, CE and DE. Play around with your construction and see if you can discover this relationship. This may take a little time, so you should not give up too easily.

Need a hint as to what you are looking for? Use this only as a last resort. (Requires GSP 4.0)

Prove any conjecture that you make. (Hint for the proof?)