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X₂₀₅¶

X₉-CEVA CONJUGATE OF X₃₁

X₂₀₅ (X₉-CEVA CONJUGATE OF X₃₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_205 = X_9-CEVA CONJUGATE OF X_31."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            mittenpunkt_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00205(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_205 = X_9-CEVA CONJUGATE OF X_31 on reference triangle ABC."""
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center"])
            X_205 = ceva_conjugate(model, A, B, C, X_9, X_31, ID="X_205", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_25, X_41, 25, 41, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            central_line(model, X_37, X_48, 37, 48, incident=True)
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_78, X_101, 78, 101, incident=True)
            return promote_point_to_top(model, X_205)


        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_205 on the given reference triangle."""
            model = create_model('X_205 = X_9-CEVA CONJUGATE OF X_31')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00205(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-00205.json"))
            write_center_svg(
                model_acute,
                here / "x-00205.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X205¶

X₂₀₅¶