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X₂₇₈₅¶

ISOGONAL CONJUGATE OF X₂₇₀₁

X₂₇₈₅ is the isogonal conjugate of X₂₇₀₁.

X₂₇₈₅ (ISOGONAL CONJUGATE OF X₂₇₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2785 = ISOGONAL CONJUGATE OF X_2701."""

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


        def construct_x_02785(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2785 = ISOGONAL CONJUGATE OF X_2701 on reference triangle ABC."""
            X_2701 = eval_trilinear_point(model, A, B, C, '(a/((b - c)*(a**(3) + b**(3) + c**(3) - 2*a**(2)*b - 2*a**(2)*c + a*b*c)))', ID="X_2701", classes=["center"])
            X_2785 = isogonal_conjugate(model, A, B, C, X_2701, ID="X_2785", classes=["selected", "target"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center", "incident"])
            central_line(model, X_98, X_102, 98, 102, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_99, X_109, 99, 109, incident=True)
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            X_117 = point_from_barycentrics(model, A, B, C, 0.19223485, -0.017045455, 0.82481061, ID="X_117", classes=["center", "incident"])
            central_line(model, X_114, X_117, 114, 117, incident=True)
            return promote_point_to_top(model, X_2785)


        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_2785 on the given reference triangle."""
            model = create_model('X_2785 = ISOGONAL CONJUGATE OF X_2701')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02785(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-02785.json"))
            write_center_svg(
                model_acute,
                here / "x-02785.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2785¶

X₂₇₈₅¶