Τρίτη 19 Μαρτίου 2013

POINT ON THE CIRCUMCIRCLE

Let ABC be a triangle, A'B'C', A"B"C" the antipedal tiangles of H, O [antimedial, tangential, resp.].

The triangles:

3. ABC, Triangle A*B*C* bounded by the lines (A'A",B'B",C'C") are perspective.

[the perspector is on the circumcircle(ABC) = NPC(A'B'C') = Incircle(A"B"C")]

Coordinates?

Antreas P. Hatzipolakis, Hyacinthos #21780

Generalization

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X(72413) = X(1296)X(66615)∩X(8705)X(10098) Barycentrics    a^2*(2*a^10+2*b^10-b^8*c^2-11*b^6*c^4+5*b^4*c^6+9*b^2*c^8-4*c^10-a^8*(8*b^2...