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X₃₃₁₆¶

ISOGONAL CONJUGATE OF X₃₃₁₁

X₃₃₁₆ is the isogonal conjugate of X₃₃₁₁.

X₃₃₁₆ (ISOGONAL CONJUGATE OF X₃₃₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3316 = ISOGONAL CONJUGATE OF X_3311."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03316(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3316 = ISOGONAL CONJUGATE OF X_3311 on reference triangle ABC."""
            X_3311 = eval_trilinear_point(model, A, B, C, 'cos(A) + 2*sin(A)', ID="X_3311", classes=["center"])
            X_3316 = isogonal_conjugate(model, A, B, C, X_3311, ID="X_3316", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_590 = eval_trilinear_point(model, A, B, C, '(a**(2) + 4*area )/a', ID="X_590", classes=["center", "incident"])
            central_line(model, X_4, X_590, 4, 590, incident=True)
            X_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center", "incident"])
            X_631 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B)*cos(C)', ID="X_631", classes=["center", "incident"])
            central_line(model, X_485, X_631, 485, 631, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_1131 = eval_trilinear_point(model, A, B, C, '1/(sin(A) + 2*cos(A))', ID="X_1131", classes=["center", "incident"])
            central_line(model, X_3, X_1131, 3, 1131, incident=True)
            return promote_point_to_top(model, X_3316)


        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_3316 on the given reference triangle."""
            model = create_model('X_3316 = ISOGONAL CONJUGATE OF X_3311')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03316(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-03316.json"))
            write_center_svg(
                model_acute,
                here / "x-03316.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3316¶

X₃₃₁₆¶