# IM2.7 T8 Angles formed by Secants (outside)

Topic:
Angles
In the last task, you found a relationship between the angle formed by two tangent lines that intersect outside of a circle and the arc they intercept. This task will extend that reasoning to secant lines. ﻿ Interact with the applet below for a few minutes. Then answer the questions that follow. Be sure to change the locations of the BIG POINTS each time before you slide the slider.

1) Suppose the pink arc measures 200 degrees and the green arc measures 50 degrees. What would the measure of the blue angle be? 2) Move the pink points so that only 1 of the rays becomes tangent to the circle (while keeping the other ray a secant ray.) Answer question #1 again within this context. 3) Move the pink points so that both rays become tangent to the circle. Suppose, in this case, the entire pink arc measures 210 degrees. What would the measure of the green arc be? What would the measure of the blue angle be? 4) Next, move the blue point as close to the circle as possible so that the green arc almost disappears. (It won't disappear entirely). Keep the blue point on the circle. Now slowly re-slide the slider again. What previously learned theorem do these transformations reveal? 5) Suppose 2 secant rays (drawn from a point outside a circle) intersect the circle above so that the blue angle measures 60 degrees and the entire pink arc measures 200 degrees. If this is the case, what would the measure of the entire green arc be? 6) Answer question number 5 again, this time in the case of a secant and a tangent.