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?
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