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Nikolaos Dergiades, Harmonic conjugate circles relative to a triangle,
Forum Geometricorum, 12 (2012) 153--159.
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Abstract. We use the term harmonic conjugate conics, for the conics C, C* with equations

C: fx2+gy2+hz2+2pyz+2qz+2rxy = 0 and C*: fx2+gy2+hz2-2pyz-2qz-2rxy = 0, in barycentric coordinates because if A_1, A_2 are the points where C meets the sideline BC of the reference triangle ABC, then C* meets the same side at the points A_1', A_2' that are harmonic conjugates of A_1, A_2 respectively relative to BC and similarly for the other sides of ABC. So we investigate the interesting case where both C and C* are circles.

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