Day 7: Lines and Circles

Investigation 1: Construct a circle and four points on that circle. Label the four points A, B, C and D. Construct secant lines AD and BC such that the lines intersect in the interior of the circle. Label the point of intersection E. Measure angle CED, arc measure AB and arc measure CD. (We say that angle CED intercepts arc CD.) Find a relationship between these measures. Prove your conjecture.

Investigation 2: Using the same GSP sketch from above, drag point A around the circle until E is on the exterior of the circle and reevaluate the relationship between the angle formed by the intersecting secants and the intercepted arcs. Prove your conjecture.
Investigation 3: What happens when E lies on the circle?