← etc / Encyclopedia of Triangle Centers

X₂₉₁₄¶

ORTHIC-ISOGONAL CONJUGATE OF X₁₈₆

X₂₉₁₄ is the orthic-isogonal conjugate of X₁₈₆.

X₂₉₁₄ (ORTHIC-ISOGONAL CONJUGATE OF X₁₈₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2914 = ORTHIC-ISOGONAL CONJUGATE OF X_186."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02914(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2914 = ORTHIC-ISOGONAL CONJUGATE OF X_186 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_186 = eval_trilinear_point(model, A, B, C, '4*cos(A) - sec(A)', ID="X_186", classes=["center"])
            X_2914 = ceva_conjugate(model, A, B, C, X_4, X_186, ID="X_2914", classes=["selected", "target"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_54, X_74, 54, 74, incident=True)
            X_52 = eval_trilinear_point(model, A, B, C, 'cos(2*A)*cos(B - C)', ID="X_52", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_52, X_110, 52, 110, incident=True)
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center", "incident"])
            central_line(model, X_4, X_195, 4, 195, incident=True)
            return promote_point_to_top(model, X_2914)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_2914 on the given reference triangle."""
            model = create_model('X_2914 = ORTHIC-ISOGONAL CONJUGATE OF X_186')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02914(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-02914.json"))
            write_center_svg(
                model_acute,
                here / "x-02914.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2914¶

X₂₉₁₄¶