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X₂₆₇¶

ISOGONAL CONJUGATE OF X₁₉₁

X₂₆₇ (ISOGONAL CONJUGATE OF X₁₉₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_267 = ISOGONAL CONJUGATE OF X_191."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00267(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_267 = ISOGONAL CONJUGATE OF X_191 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_229 = point_from_barycentrics(model, A, B, C, 0.21061481, 0.29086323, 0.49852195, ID="X_229", classes=["center"])
            X_267 = reflection_in_point(model, X_1, X_229, ID="X_267", classes=["selected", "target"], guide=False)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_35, X_37, 35, 37, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center", "incident"])
            central_line(model, X_10, X_191, 10, 191, incident=True)
            central_line(model, X_1, X_229, 1, 229, incident=True)
            return promote_point_to_top(model, X_267)


        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_267 on the given reference triangle."""
            model = create_model('X_267 = ISOGONAL CONJUGATE OF X_191')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00267(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-00267.json"))
            write_center_svg(
                model_acute,
                here / "x-00267.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X267¶

X₂₆₇¶