Forum Geometricorum, 8 (2008) 151--155.

Abstract: In this paper we further extend the generalization of the concept of Gergonne point for circles concentric to the inscribed circle. Given a triangle V_1V_2V_3, a point I and three arbitrary directions q_1, q_2, q_3 from I, we find a distance x=IQ_1=IQ_2=IQ_3 along these directions, for which the three cevians V_iQ_i are concurrent. Types and number of solutions, which can be obtained by the common intersection points of three conics, are also discussed in detail.

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