Intersecting Chords Theorem
Slide points A, B, C, D to illustrate the result. It is important to notice that lengths are always measured to the intersection of the chords regardless of whether this intersection is inside or outside the circle. Circle Theorems http://www.geogebratube.org/student/c89/m1462/yryy
You might want to look at the special cases when the points coincide and tangents to the circle are created. Does this change the result?