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X₄₄₅¶

EULER X₇₉-10th-SUBSTITUTION POINT

X₄₄₅ = isotomic conjugate of the isogonal conjugate of X₄₄₀₉₅

X₄₄₅ (EULER X₇₉-10th-SUBSTITUTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_445 = EULER X_79-10th-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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00445(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_445 = EULER X_79-10th-SUBSTITUTION POINT on reference triangle ABC."""
            X_445 = eval_barycentric_point(model, A, B, C, '(a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) - b*c - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(2)*b - b**(3) + a**(2)*c + 2*a*b*c + b**(2)*c + b*c**(2) - c**(3))', ID="X_445", 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_281 = eval_trilinear_point(model, A, B, C, 'sec(A)*cot(A/2)', ID="X_281", classes=["center", "incident"])
            X_3580 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(6) + c**(6) + (a**(4) - b**(2)*c**(2))*(b**(2) + c**(2)) - 2*a**(2)*(b**(4) + c**(4)) + 2*a**(2)*b**(2)*c**(2))', ID="X_3580", classes=["center", "incident"])
            central_line(model, X_281, X_3580, 281, 3580, incident=True)
            X_340 = eval_trilinear_point(model, A, B, C, 'sec(A)*sin(3*A)*(csc(A))**(3)', ID="X_340", classes=["center", "incident"])
            X_3578 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a + b + c)*(a**(2) - b**(2) - c**(2) - b*c))', ID="X_3578", classes=["center", "incident"])
            central_line(model, X_340, X_3578, 340, 3578, incident=True)
            return promote_point_to_top(model, X_445)


        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_445 on the given reference triangle."""
            model = create_model('X_445 = EULER X_79-10th-SUBSTITUTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00445(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-00445.json"))
            write_center_svg(
                model_acute,
                here / "x-00445.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X445¶

X₄₄₅¶