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X₈₉₁¶

ISOTOMIC CONJUGATE OF X₈₈₉

As the isogonal conjugate of a point on the circumcircle, X₈₉₁ lies on the line at infinity.

X₈₉₁ (ISOTOMIC CONJUGATE OF X₈₈₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_891 = ISOTOMIC CONJUGATE OF X_889."""

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


        def construct_x_00891(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_891 = ISOTOMIC CONJUGATE OF X_889 on reference triangle ABC."""
            X_891 = eval_trilinear_point(model, A, B, C, '(b - c)*(a*b + a*c - 2*b*c)', ID="X_891", 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_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_659 = eval_trilinear_point(model, A, B, C, '(a**(2) - b*c)*(b - c)', ID="X_659", classes=["center", "incident"])
            central_line(model, X_1, X_659, 1, 659, incident=True)
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            central_line(model, X_244, X_665, 244, 665, incident=True)
            return promote_point_to_top(model, X_891)


        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_891 on the given reference triangle."""
            model = create_model('X_891 = ISOTOMIC CONJUGATE OF X_889')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00891(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-00891.json"))
            write_center_svg(
                model_acute,
                here / "x-00891.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X891¶

X₈₉₁¶