Segments of Intersecting Chords

Drag points A, B, C, and D to change the segment lengths.[br]Do you see any relationship between the lengths of the segments formed by the two intersecting chords?[br][br]Click the first check box to show the similar triangles.[br]What is the scale factor between the two triangles?[br][br]Click the second check box to show the scale factor proportion.[br]What happens if you cross-multiply the proportion?[br][br]Click the third check box to show the products of the segments formed by the intersecting chords.[br]Do the products always seem to be the same?[br]How could you prove your conclusion?