Forum Geometricorum, 5 (2005) 149--164.

Abstract: Consider a triangle ABC with excircles (I_a), (I_b), (I_c), tangent to the nine-point circle respectively at F_a, F_b, F_c. Consider also the polars of A, B, C with respect to the corresponding excircles, bounding a triangle XYZ. We present, among other results, synthetic proofs of (i) the perspectivity of XYZ and F_aF_bF_c at the complement of the Schiffler point of ABC, (ii) the concurrency at the same point of the radical axes of the nine-point circles of triangles I_aBC, I_bCA, and I_cAB.

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