Forum Geometricorum, 5 (2005) 65--74.

Abstract: In this note, we prove that for every triangle ABC, there exists a unique interior point M the cevians AA', BB', and CC' through which have the property that angle AC'B' = angle BA'C' = angle CB'A', and a unique interior pointÂ M' the cevians AA', BB', and CC' through which have the property that angle AB'C' = angle BC'A' = angle CA'B'. We study some properties of these Brocard-like points, and characterize those centers for which the angles AC'B', BA'C', and CB'A' are linear forms in the angles A, B, and C of ABC.

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