Investigation 1: What happens when two tangents intersect in the exterior of a circle? Begin by constructing circle A. Construct two points C and D on circle A. Construct the line perpendicular to radius AC at C, and then repeat for radius AD and point D. (Review: The lines you just constructed are tangent to circle A. Why?) Drag points C and D until the two tangent lines intersect in the exterior of the circle. Your construction should be similar to the following:

Now construct a point F on circle A as shown below:

Measure arc CFD, arc CD and angle CED. Find a relationship between the measures. Proof?

Investigation 2: Perform a similar investigation for a secant and a tangent that intersect in the exterior of a circle. Proof?

Investigation 3: Perform a similar investigation for a secant and a tangent that intersect on the circle. Proof?