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X₃₂₀₅¶

X₅₄-CEVA CONJUGATE OF X₆₁

X₃₂₀₅ (X₅₄-CEVA CONJUGATE OF X₆₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3205 = X_54-CEVA CONJUGATE OF X_61."""

        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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03205(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3205 = X_54-CEVA CONJUGATE OF X_61 on reference triangle ABC."""
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center"])
            X_61 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /6)', ID="X_61", classes=["center"])
            X_3205 = ceva_conjugate(model, A, B, C, X_54, X_61, ID="X_3205", classes=["selected", "target"])
            X_14 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /3)', ID="X_14", classes=["center", "incident"])
            central_line(model, X_14, X_54, 14, 54, incident=True)
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            central_line(model, X_49, X_61, 49, 61, incident=True)
            X_17 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /6)', ID="X_17", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_17, X_110, 17, 110, incident=True)
            return promote_point_to_top(model, X_3205)


        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_3205 on the given reference triangle."""
            model = create_model('X_3205 = X_54-CEVA CONJUGATE OF X_61')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03205(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-03205.json"))
            write_center_svg(
                model_acute,
                here / "x-03205.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3205¶

X₃₂₀₅¶