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X₁₂₁₆¶

ISOGONAL CONJUGATE OF X₁₁₇₉

X₁₂₁₆ is the isogonal conjugate of X₁₁₇₉.

X₁₂₁₆ (ISOGONAL CONJUGATE OF X₁₁₇₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1216 = ISOGONAL CONJUGATE OF X_1179."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01216(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1216 = ISOGONAL CONJUGATE OF X_1179 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_52 = eval_trilinear_point(model, A, B, C, 'cos(2*A)*cos(B - C)', ID="X_52", classes=["center"])
            central_line(model, X_3, X_49, 3, 49)
            central_line(model, X_2, X_52, 2, 52)
            X_1216 = intersect_lines(model, X_3, X_49, X_2, X_52, ID="X_1216", classes=["selected", "target"])
            X_68 = eval_trilinear_point(model, A, B, C, 'cos(A)*sec(2*A)', ID="X_68", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_68, X_69, 68, 69, incident=True)
            return promote_point_to_top(model, X_1216)


        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_1216 on the given reference triangle."""
            model = create_model('X_1216 = ISOGONAL CONJUGATE OF X_1179')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01216(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-01216.json"))
            write_center_svg(
                model_acute,
                here / "x-01216.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1216¶

X₁₂₁₆¶