Nikolaos Dergiades and Juan Carlos Salazar,  Harcourt's theorem,

Forum Geometricorum, 3 (2003) 117--124.

Abstract:  We give a proof of Harcourt's theorem that if the signed distances from the vertices of a triangle of sides a, b, c to a
tangent of the incircle are a_1, b_1, c_1, then aa_1 + bb_1 + cc_1 is twice of the area of the triangle. We also show  that there is a point on the circumconic with center I whose  distances to the sidelines of ABC are precisely a_1, b_1, c_1. An application is given to the extangents triangle formed by the external common tangents of the excircles.

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