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.