Sadi Abu-Saymeh and Mowaffaq Hajja, Some Brocard-like
points of a triangle,
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.
[ps file] [pdf file]
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