Jean-Pierre Ehrmann, An affine variant of a Steinhaus problem,
Forum Geometricorum, 8 (2008) 1--5.

Abstract: Given a triangle ABC and three positive real numbers u, v, w, we prove that there exists a unique point P in the interior of the triangle, with cevian triangle P_aP_bP_c, such that the areas of the three quadrilaterals PP_bAP_c, PP_cBP_a, PP_aCP_b are in the ratio u : v : w. We locate P as an intersection of three hyperbolas.

[ps file][pdf]