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X₄₁₁¶

EULER X₂₁-2nd-SUBSTITUTION POINT

X₄₁₁ = ABC-to-excentral barycentric image of X₁₂

X₄₁₁ (EULER X₂₁-2nd-SUBSTITUTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_411 = EULER X_21-2nd-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_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00411(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_411 = EULER X_21-2nd-SUBSTITUTION POINT on reference triangle ABC."""
            X_411 = eval_trilinear_point(model, A, B, C, '(cos(B)*cos(C) - (cos(A) + cos(B) + cos(C))*cos(A))', ID="X_411", 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_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            central_line(model, X_40, X_78, 40, 78, incident=True)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_35, X_516, 35, 516, incident=True)
            return promote_point_to_top(model, X_411)


        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_411 on the given reference triangle."""
            model = create_model('X_411 = EULER X_21-2nd-SUBSTITUTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00411(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-00411.json"))
            write_center_svg(
                model_acute,
                here / "x-00411.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X411¶

X₄₁₁¶