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X₁₂₄₄¶

ISOGONAL CONJUGATE OF X₁₀₀₉

X₁₂₄₄ is the isogonal conjugate of X₁₀₀₉.

X₁₂₄₄ (ISOGONAL CONJUGATE OF X₁₀₀₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1244 = ISOGONAL CONJUGATE OF X_1009."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01244(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1244 = ISOGONAL CONJUGATE OF X_1009 on reference triangle ABC."""
            X_1009 = eval_trilinear_point(model, A, B, C, '(a**(4)*(b + c) + 2*a**(3)*b*c - a**(2)*(b**(3) + c**(3)) + b*c*(b + c)*(b**(2) + c**(2)))', ID="X_1009", classes=["center"])
            X_1244 = isogonal_conjugate(model, A, B, C, X_1009, ID="X_1244", classes=["selected", "target"])
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            central_line(model, X_71, X_238, 71, 238, incident=True)
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_239 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - b*c)', ID="X_239", classes=["center", "incident"])
            central_line(model, X_72, X_239, 72, 239, incident=True)
            return promote_point_to_top(model, X_1244)


        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_1244 on the given reference triangle."""
            model = create_model('X_1244 = ISOGONAL CONJUGATE OF X_1009')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01244(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-01244.json"))
            write_center_svg(
                model_acute,
                here / "x-01244.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1244¶

X₁₂₄₄¶