Can You Inscribe This Quadrilateral? (Analytic Geometry)

At first glance, it looks like a standard analytic geometry problem: trace the locus of a moving point, intersect a circle, and pin down the coordinates. But once you connect the dots, a much deeper puzzle emerges. Can this quadrilateral actually be inscribed inside a circle—or does the algebra lead straight into a trap?

In this video, we break down the math step-by-step, unlocking hidden symmetries using Thales’s theorem, coordinate proofs, and dynamic visual animations. Grab a pen and paper—let’s see if your intuition holds up before the final proof reveals the answer!