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X₄₂₆¶

EULER X₁₉-4th-SUBSTITUTION POINT

X₄₂₆ = isogonal conjugate of the isotomic conjugate of X₄₄₁₄₁

X₄₂₆ (EULER X₁₉-4th-SUBSTITUTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_426 = EULER X_19-4th-SUBSTITUTION POINT."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00426(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_426 = EULER X_19-4th-SUBSTITUTION POINT on reference triangle ABC."""
            X_426 = eval_barycentric_point(model, A, B, C, '(a + b) * (a + c) * (a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(6) - a**(5)*b - a**(4)*b**(2) + a**(3)*b**(3) - a**(5)*c + a**(4)*b*c + a**(3)*b**(2)*c - b**(5)*c - a**(4)*c**(2) + a**(3)*b*c**(2) + 2*a**(2)*b**(2)*c**(2) - 2*a*b**(3)*c**(2) + a**(3)*c**(3) - 2*a*b**(2)*c**(3) + 2*b**(3)*c**(3) - b*c**(5))', ID="X_426", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_157 = eval_trilinear_point(model, A, B, C, '(a*(b**(3)*cos(B) + c**(3)*cos(C) - a**(3)*cos(A)))', ID="X_157", classes=["center", "incident"])
            X_1853 = point_from_barycentrics(model, A, B, C, -0.10818713, -0.21754386, 1.325731, ID="X_1853", classes=["center", "incident"])
            central_line(model, X_157, X_1853, 157, 1853, incident=True)
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            X_2351 = eval_trilinear_point(model, A, B, C, 'a*tan(2*A)', ID="X_2351", classes=["center", "incident"])
            central_line(model, X_125, X_2351, 125, 2351, incident=True)
            return promote_point_to_top(model, X_426)


        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_426 on the given reference triangle."""
            model = create_model('X_426 = EULER X_19-4th-SUBSTITUTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00426(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-00426.json"))
            write_center_svg(
                model_acute,
                here / "x-00426.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X426¶

X₄₂₆¶