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(72934) = (name pending) Barycentrics    a ((a^2+b^2-c^2) (a^2-b^2+c^2) (a^9 b^3-a^8 b^4-3 a^7 b^5+3 a^6 b^6+3 a^5 b^7-3 a^4 b^8-a^3 b^9+...