This applet is designed to help you gather data to discover the angle relationships for when a tangent-secant intersect a circle. Points T, Q, and R can be manipulated to change the size of the arcs with the size of <TPQ being updated as a result. Point B can be used to change the size of the circle.
Record the size of arc TR, arc TQ and the <TPR. Look for relationships between the angles. Check for relationships like adding the arc measures, the average of the arc measures, subtracting the arc measures, dividing results in half, angles being complementary, supplementary, or adding to 360. Check for combinations of these relationships. The goal is to calculate x based on the arc measures.