[1] Lines {L, P

[2] Define point O as the intersection of L with the medial of B'C'. Triangles OC'P

In fact, they have equal sides, since OC'=OB', OP

[3] It follows that quadrangles OQP

[4] It follows also that AP

[1] Note that line L'' (not drawn), which is parallel to L from P, passes also from a fixed point A', which is the diametral of A on the circumcircle of ABC (A'P is parallel and double in length to OQ).

[2] One can carry out the construction of L and L' (orthogonal to L at Q) also for generic triangles. In that case line L' envelopes a parabola, known as the

[3] In the generic case L envelopes also a parabola, which for isosceli degenerates to a point as shown. For a discussion on these parabolas see the file Artzt_Generation.html .

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