Forum Geometricorum, 5 (2005) 33--36.

Abstract: Let ABC be a triangle with side-lengths a, b, and c, and with angles A, B, and C. Let AA', BB', and CC' be the cevians through a point V, let x, y, and z be the lengths of the segments BA', CB', and AC', and let xi, eta, and zeta be the measures of the angles BAA', CBB', and ACC'. The centers V for which x, y, and z are linear forms in a, b, and c are characterized. So are the centers for which xi, eta, and zeta are linear forms in A, B, and C.

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