I created a set of instructions for a student led investigation of the conclusions for tangents to circles and the angles and arcs formed by chords. Most students were able to follow the instructions for the construction, but struggle with the conclusions. At least with the tangent half of the exercise, some students did make some relevant conclusions, but the chord angle/arc equation eluded everyone.
Additionally, I made applets in GeoGebra for students to play around with and get around making the construction themselves (and also to help guide them toward the conclusions).
Tangents to Circles
Arcs and Angles formed by Chords