Use GSP 4.0 to perform the following
Step 1: Construct two points. Label these points A and B. Construct the circle with center A that passes through B.
Step 2: Construct a point on circle A. Label this point C. Construct a point D somewhere on the exterior of circle A. Construct line CD.
Step 3: In all likelihood, line CD is a secant of circle A. Measure angle ACD. Drag point C until line CD becomes tangent to circle A. Observations?
Step 4: Prove your conjecture. Hint?
Extension: What would the converse of this
theorem be? Is this converse true?
Using the results of investigation 1, draw a circle and contruct two lines that are tangent to this circle. Adjust your sketch until the tangents intersect at a point X. If the points of tangency are M and N, what appears to be true about MX and NX? Measure these values and try tragging different points.
Conjecture? Proof? Hint?