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X₈₈₈¶

ISOTOMIC CONJUGATE OF X₈₈₆

As the isogonal conjugate of a point on the circumcircle, X₈₈₈ lies on the line at infinity.

X₈₈₈ (ISOTOMIC CONJUGATE OF X₈₈₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_888 = ISOTOMIC CONJUGATE OF X_886."""

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


        def construct_x_00888(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_888 = ISOTOMIC CONJUGATE OF X_886 on reference triangle ABC."""
            X_886 = eval_barycentric_point(model, A, B, C, 'b**(2)*c**(2)/((b**(2) - c**(2))*(a**(2)*b**(2) + a**(2)*c**(2) - 2*b**(2)*c**(2)))', ID="X_886", classes=["center"])
            X_888 = isotomic_conjugate(model, A, B, C, X_886, ID="X_888", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_351 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(2) + c**(2) - 2*a**(2)))', ID="X_351", classes=["center", "incident"])
            X_865 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*(csc(C))**(2)*sin(C - A)*csc(A - B) - sin(2*C)*(csc(B))**(2)*sin(B - A)*csc(A - C))', ID="X_865", classes=["center", "incident"])
            central_line(model, X_351, X_865, 351, 865, incident=True)
            X_694 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) - b**(2)*c**(2))', ID="X_694", classes=["center", "incident"])
            X_882 = point_from_barycentrics(model, A, B, C, 0.023590899, 1.0060979, -0.02968882, ID="X_882", classes=["center", "incident"])
            central_line(model, X_694, X_882, 694, 882, incident=True)
            return promote_point_to_top(model, X_888)


        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_888 on the given reference triangle."""
            model = create_model('X_888 = ISOTOMIC CONJUGATE OF X_886')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00888(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-00888.json"))
            write_center_svg(
                model_acute,
                here / "x-00888.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X888¶

X₈₈₈¶