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X₈₂₁¶

ISOGONAL CONJUGATE OF X₈₂₀

X₈₂₁ (ISOGONAL CONJUGATE OF X₈₂₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_821 = ISOGONAL CONJUGATE OF X_820."""

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


        def construct_x_00821(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_821 = ISOGONAL CONJUGATE OF X_820 on reference triangle ABC."""
            X_820 = eval_trilinear_point(model, A, B, C, '((cos(A))**(2)*((cos(B))**(2) + (cos(C))**(2)))', ID="X_820", classes=["center"])
            X_821 = isogonal_conjugate(model, A, B, C, X_820, ID="X_821", classes=["selected", "target"])
            X_158 = eval_trilinear_point(model, A, B, C, '(sec(A))**(2)', ID="X_158", classes=["center", "incident"])
            X_255 = eval_trilinear_point(model, A, B, C, '(cos(A))**(2)', ID="X_255", classes=["center", "incident"])
            central_line(model, X_158, X_255, 158, 255, incident=True)
            X_243 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(2) - cos(B)*cos(C))', ID="X_243", classes=["center", "incident"])
            X_411 = eval_trilinear_point(model, A, B, C, '(cos(B)*cos(C) - (cos(A) + cos(B) + cos(C))*cos(A))', ID="X_411", classes=["center", "incident"])
            central_line(model, X_243, X_411, 243, 411, incident=True)
            X_774 = eval_trilinear_point(model, A, B, C, '(cos(B))**(2) + (cos(C))**(2)', ID="X_774", classes=["center", "incident"])
            X_823 = eval_trilinear_point(model, A, B, C, '1/((sec(B))**(2) - (sec(C))**(2))', ID="X_823", classes=["center", "incident"])
            central_line(model, X_774, X_823, 774, 823, incident=True)
            return promote_point_to_top(model, X_821)


        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_821 on the given reference triangle."""
            model = create_model('X_821 = ISOGONAL CONJUGATE OF X_820')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00821(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-00821.json"))
            write_center_svg(
                model_acute,
                here / "x-00821.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X821¶

X₈₂₁¶