The Common Core Standard in question:
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
The justification, solution and scoring:
Student reactions to this kind of problem:
An alternative, more tradition proof:
Which proof do you like better?
Use transformations to prove that the two proofs are (or aren't) similar.