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X₃₄₃₅¶

X₈-VERTEX CONJUGATE OF X₈

X₃₄₃₅ (X₈-VERTEX CONJUGATE OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3435 = X_8-VERTEX CONJUGATE OF X_8."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03435(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3435 = X_8-VERTEX CONJUGATE OF X_8 on reference triangle ABC."""
            X_3435 = eval_barycentric_point(model, A, B, C, 'a**(2)/(a**(4) + 2*a**(2)*b*c - 2*a*b*c*(b + c) - (b**(2) - c**(2))**(2))', ID="X_3435", classes=["selected", "target"])
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_24, X_104, 24, 104, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_197 = eval_trilinear_point(model, A, B, C, 'a*(-a**(2)*tan(A/2) + b**(2)*tan(B/2) + c**(2)*tan(C/2))', ID="X_197", classes=["center", "incident"])
            central_line(model, X_8, X_197, 8, 197, incident=True)
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            X_836 = eval_trilinear_point(model, A, B, C, '(sin(B)*(sec(B))**(2) + sin(C)*(sec(C))**(2))', ID="X_836", classes=["center", "incident"])
            central_line(model, X_48, X_836, 48, 836, incident=True)
            return promote_point_to_top(model, X_3435)


        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_3435 on the given reference triangle."""
            model = create_model('X_3435 = X_8-VERTEX CONJUGATE OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03435(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-03435.json"))
            write_center_svg(
                model_acute,
                here / "x-03435.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3435¶

X₃₄₃₅¶