Secant Secant Segment Relationship

This applet is designed to help students gather data to find the relationship between the length of segments in a secant-secant arrangement.
Move points Q, R, S, and T to change the size of the intercepted arcs. As you do that, the size of the line segments will be updated. Collect at least 5 sets of data and look for relationships. Think about adding lengths, subtracting lengths, and multiplying lengths. Think about drawing some auxiliary lines to create triangles. Are any triangles similar to each other?