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X₂₀₆¶

X₂-CEVA CONJUGATE OF X₃₂

For another construction see Antreas P. Hatzipolakis and Peter Moses, Euclid 1713.

X₂₀₆ (X₂-CEVA CONJUGATE OF X₃₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_206 = X_2-CEVA CONJUGATE OF X_32."""

        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,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00206(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_206 = X_2-CEVA CONJUGATE OF X_32 on reference triangle ABC."""
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center"])
            X_206 = complement(model, A, B, C, X_66, ID="X_206", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_6, X_25, 6, 25, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_66, 2, 66, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", 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_69, X_110, 69, 110, incident=True)
            return promote_point_to_top(model, X_206)


        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_206 on the given reference triangle."""
            model = create_model('X_206 = X_2-CEVA CONJUGATE OF X_32')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00206(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-00206.json"))
            write_center_svg(
                model_acute,
                here / "x-00206.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X206¶

X₂₀₆¶