Monday, February 15, 2021

1659. Concurrent Lines-Equilateral Triangles

1 comment:

  1. Pa,Pb,Pc X(15) centers of BCD, CAE, ABF resp.
    Let Qa, Qb,Qc are same centers of BCD, CAE, ABF resp.
    *Lines PaQa, PbQb, PcQc concur on the circumcircle of ABC.
    **Some concurrency points:
    If Qa,Qb,Qc are X(1) incenters, concurrency point is X(100).
    If Qa,Qb,Qc are X(2) centroids concurrency point is X(476)-Tixier Point..
    If Qa,Qb,Qc are X(3) circumcenters, concurrency point is X(110).
    If Qa,Qb,Qc are X(4) orthocenters concurrency point is X(930).
    If Qa,Qb,Qc are X(5) NPC centers, concurrency point is X(925).
    If Qa,Qb,Qc are X(13) Fermat points, concurrency point is X(99)-Steiner point.

    ** *Is there any properties concurrency point for .Qa,Qb,Qc are Gergonne, Nagel centers?

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