Products Determined by a Point on the Circumcircle
Let ABC be a triangle and P be a point on the circumcircle of circumradius . Let A' and B' be the perpendicular projections of P onto BC and CA, respectively. Let Q be the perpendicular projection of P onto A'B'. Then .[more]
Drag the brown points to change the figure.[less]
See problem 5.89 in V. Prasolov, Problems in Plane and Solid Geometry, Vol. 1, Plane Geometry [PDF], (D. Leites, ed. and trans.).