# Inscribed angle theorem

0. Please drag each point. What do you notice? What do you wonder?

1. What is the relationship between the inscribed angle and the central angle that intercepts the same arc? How to see it visually, without using numbers or angle measures as such? Can be this be proof? What is a proof without words?

2. Use the Angle tool to find and display the measure of the inscribed angle and the central angle. What is the relationship between these two angles? Is this a verification or proof?

3. What are the special cases of this theorem? The angle in a semicircle or Thales' Theorem? The tangent-secant theorem? What else?

4. What happens when the central angle is more than 180 degrees? Does this theorem hold true when the central angle is a reflex angle? What new relationships can we find?

5. Does it have any connection with the cyclic quadrilateral?