Intersecting Chords
The intersecting chords property is one of my favorite bits of weird circle geometry. A brief twitter conversation with Ilana Horn and Henri Picciotto about it got me wondering how to make a sketch that emphasized the connection with the Inscribed Angle Theorem.
So this sketch has four free points on the circle, that allows you to see the similar triangles, and observe the equal ratios or products that are the result. Whether the intersection point is interior (intersecting chords) or exterior (a secant pair).