Some Brocard-likepoints of a triangle

摘要

  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 point  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.