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X₂₄₄₅¶

ISOGONAL CONJUGATE OF X₂₄₁₉

X₂₄₄₅ is the isogonal conjugate of X₂₄₁₉.

X₂₄₄₅ (ISOGONAL CONJUGATE OF X₂₄₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2445 = ISOGONAL CONJUGATE OF X_2419."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02445(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2445 = ISOGONAL CONJUGATE OF X_2419 on reference triangle ABC."""
            X_2419 = point_from_barycentrics(model, A, B, C, -80.557045, 75.491805, 6.0652396, ID="X_2419", classes=["center"])
            X_2445 = isogonal_conjugate(model, A, B, C, X_2419, ID="X_2445", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_6, X_25, 6, 25, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_1301 = point_from_barycentrics(model, A, B, C, -0.036707118, 0.057047829, 0.97965929, ID="X_1301", classes=["center", "incident"])
            central_line(model, X_110, X_1301, 110, 1301, incident=True)
            X_250 = eval_trilinear_point(model, A, B, C, '(sec(A))*(csc(B - C))**(2)', ID="X_250", classes=["center", "incident"])
            X_2421 = eval_trilinear_point(model, A, B, C, '(sin(A))*(sin(2*B) + sin(2*C) - 2*(cot(A))*((sin(B))**(2) + (sin(C))**(2)))/(cot(B) - cot(C))', ID="X_2421", classes=["center", "incident"])
            central_line(model, X_250, X_2421, 250, 2421, incident=True)
            return promote_point_to_top(model, X_2445)


        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_2445 on the given reference triangle."""
            model = create_model('X_2445 = ISOGONAL CONJUGATE OF X_2419')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02445(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-02445.json"))
            write_center_svg(
                model_acute,
                here / "x-02445.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2445¶

X₂₄₄₅¶