Tangent-Secant segment relationships

This applet is designed to help students gather data to discover the relationship between between the length of the line segments when a tangent and a secant intersect a circle. Points T, Q, P and R can all be manipulated to vary the size of the arcs and lengths of the segments.
Vary the values of a, b, and c. Record at least 5 sets of data. Look for relationships between the lengths. Think about adding lengths, subtracting lengths, multiplying lengths. Can you create similar figures by drawing in auxiliary lines?