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X₃₁₆₁¶

X₂-CEVA CONJUGATE OF X₈

X₃₁₆₁ = perspector of triangle ABC and the tangential triangle of the conic that passes through A, B, C and has center X₈

X₃₁₆₁ (X₂-CEVA CONJUGATE OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3161 = X_2-CEVA 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            crosspoint,
            eval_trilinear_point,
            mittenpunkt_of,
            nagel_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03161(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3161 = X_2-CEVA CONJUGATE OF X_8 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center"])
            X_3161 = crosspoint(model, A, B, C, X_2, X_145, ID="X_3161", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            central_line(model, X_8, X_9, 8, 9, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_344 = eval_trilinear_point(model, A, B, C, '((csc(A/2))**(2))*((cos(B/2))**(4) + (cos(C/2))**(4) - (cos(A/2))**(4))', ID="X_344", classes=["center", "incident"])
            central_line(model, X_190, X_344, 190, 344, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_644 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b - c))', ID="X_644", classes=["center", "incident"])
            central_line(model, X_6, X_644, 6, 644, incident=True)
            return promote_point_to_top(model, X_3161)


        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_3161 on the given reference triangle."""
            model = create_model('X_3161 = X_2-CEVA CONJUGATE OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03161(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-03161.json"))
            write_center_svg(
                model_acute,
                here / "x-03161.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3161¶

X₃₁₆₁¶