In: Math
Prove the following for Euclidean Geometry. Provide general dynamic illustrations in GeoGebra. You will have to break down your illustrations and your proofs into 3 cases. Case 1: Both sides of the angle are tangent to the circle. Case 2: Exactly one side of the angle is tangent to the circle. Case 3: Neither side of the angle is tangent to the circle.
Proposition 129. If an angle intercepts two arcs of a circle, then the measure of the angle is half the absolute value of the difference of the measures of the intercepted arcs.