Triangles ABC and HIJ can be considered as particular instances of a triangle SQP, pivoting around the first Brocard point of MKL. All these triangles are similar to each other and to MKL. In fact this is a basic property of the Brocard points: Its [pedal] triangles are similar to the original triangle. Triangle ABC is characterized by having its sides orthogonal to those of MKL. HIJ is characterized by having its vertices at the middles of segments CL, BM and AK. The question of when three points SPQ on the sides of a triangle MKL, define a similar to MKL triangle, pivoting around its first Brocard point, as well as another particular instance of a pivoting triangle is discussed in the file BrocardPivot.html .

In the figure above the line OD'' is the locus of the second Brocard points D' of the pivotal triangles. It passes through the symmedian point O (and circumcenter of ABC) of MKL and its second Brocard point D''. The discussion on pivots is initialized in Pivot.html .

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