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X₁₂₂₅¶

ISOTOMIC CONJUGATE OF X₁₁₆₆

X₁₂₂₅ is the isotomic conjugate of X₁₁₆₆.

X₁₂₂₅ (ISOTOMIC CONJUGATE OF X₁₁₆₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1225 = ISOTOMIC CONJUGATE OF X_1166."""

        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,
            isotomic_conjugate,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01225(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1225 = ISOTOMIC CONJUGATE OF X_1166 on reference triangle ABC."""
            X_1166 = point_from_barycentrics(model, A, B, C, 0.20424736, 0.33803917, 0.45771347, ID="X_1166", classes=["center"])
            X_1225 = isotomic_conjugate(model, A, B, C, X_1166, ID="X_1225", classes=["selected", "target"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_95 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*sec(B - C)', ID="X_95", classes=["center", "incident"])
            central_line(model, X_76, X_95, 76, 95, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_311 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*cos(B - C)', ID="X_311", classes=["center", "incident"])
            central_line(model, X_5, X_311, 5, 311, incident=True)
            X_339 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(cos(A))/a**(4)', ID="X_339", classes=["center", "incident"])
            X_1232 = point_from_barycentrics(model, A, B, C, 0.47795093, 0.32307014, 0.19897893, ID="X_1232", classes=["center", "incident"])
            central_line(model, X_339, X_1232, 339, 1232, incident=True)
            return promote_point_to_top(model, X_1225)


        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_1225 on the given reference triangle."""
            model = create_model('X_1225 = ISOTOMIC CONJUGATE OF X_1166')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01225(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-01225.json"))
            write_center_svg(
                model_acute,
                here / "x-01225.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1225¶

X₁₂₂₅¶