The Two Triangles Theorem

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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.

Contributed by: Chris Boucher (March 2011)
After work by: Larry W. Cusick
Open content licensed under CC BY-NC-SA



The theorem and the idea for the image are from: L. W. Cusick, "Archimedean Quadrature Redux," Mathematics Magazine, 81(2), 2008 p. 83.

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