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X₃₂₂₉¶

ISOGONAL CONJUGATE OF X₃₂₂₅

X₃₂₂₉ is the isogonal conjugate of X₃₂₂₅.

X₃₂₂₉ (ISOGONAL CONJUGATE OF X₃₂₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3229 = ISOGONAL CONJUGATE OF X_3225."""

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


        def construct_x_03229(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3229 = ISOGONAL CONJUGATE OF X_3225 on reference triangle ABC."""
            X_3225 = eval_trilinear_point(model, A, B, C, '(b*c/(a**(2)*b**(4) + a**(2)*c**(4) - b**(2)*c**(4) - c **(2)*b**(4)))', ID="X_3225", classes=["center"])
            X_3229 = isogonal_conjugate(model, A, B, C, X_3225, ID="X_3229", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_232 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(A +  omega  )', ID="X_232", classes=["center", "incident"])
            X_420 = eval_barycentric_point(model, A, B, C, '(a**(2) - b*c) * (a**(2) + b*c) * (a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2))', ID="X_420", classes=["center", "incident"])
            central_line(model, X_232, X_420, 232, 420, incident=True)
            return promote_point_to_top(model, X_3229)


        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_3229 on the given reference triangle."""
            model = create_model('X_3229 = ISOGONAL CONJUGATE OF X_3225')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03229(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-03229.json"))
            write_center_svg(
                model_acute,
                here / "x-03229.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3229¶

X₃₂₂₉¶