On a remarkable concurrency

  • Cosmin Pohoata, On a remarkable concurrency, Gazeta Matematica, 2 (2008), 65-70. (in Romanian) - an English version will be attached

    We give five different proofs of a concurrency due to Jean-Pierre Ehrmann (see Hyacinthos message #6966): Let ABC be a triangle and let D, E, F be the tangency points of its incircle \rho with the sides BC, CA, and AB, respectively. Draw the tangents to \rho from D, E, F (the ones different from the sidelines of ABC) and let X, Y, Z be their corresponding intersections with \rho. Then, the lines AX, BY, CZ are concurrent.

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