The Two Triangles Theorem
Let the points P, Q, and R lie on a parabola. Let P', Q', and R' be the intersection points of the tangents to the parabola at Q and R, P and R, and P and Q, respectively. The area of triangle PQR (purple) is twice the area of triangle P'Q'R' (gold). Drag the black points to change the figure.
The theorem and the idea for the image are from: L. W. Cusick, "Archimedean Quadrature Redux," Mathematics Magazine, 81(2), 2008 p. 83.