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X₂₈₂₂¶

ISOGONAL CONJUGATE OF X₂₇₃₈

X₂₈₂₂ is the isogonal conjugate of X₂₇₃₈.

X₂₈₂₂ (ISOGONAL CONJUGATE OF X₂₇₃₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2822 = ISOGONAL CONJUGATE OF X_2738."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02822(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2822 = ISOGONAL CONJUGATE OF X_2738 on reference triangle ABC."""
            X_2738 = point_from_barycentrics(model, A, B, C, 1.0098259, 0.48587606, -0.49570201, ID="X_2738", classes=["center"])
            X_2822 = isogonal_conjugate(model, A, B, C, X_2738, ID="X_2822", classes=["selected", "target"])
            X_27 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b + c)', ID="X_27", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_27, X_103, 27, 103, incident=True)
            X_118 = point_from_barycentrics(model, A, B, C, 0.28918651, -0.056547619, 0.76736111, ID="X_118", classes=["center", "incident"])
            X_122 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(cos(A) - cos(B)*cos(C))*(cot(A))**(2)', ID="X_122", classes=["center", "incident"])
            central_line(model, X_118, X_122, 118, 122, incident=True)
            X_116 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)**(2)*(b**(2) + b*c + c**(2) - a*b - a*c))', ID="X_116", classes=["center", "incident"])
            X_133 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sin(2*B) - sin(2*C))**(2) + (sin(2*A))*(sin(2*B)) + (sin(2*A))*(sin(2*C)) - 2*(sin(2*B))*(sin(2*C)))*(2*sin(2*A) - sin(2*B) - sin(2*C))', ID="X_133", classes=["center", "incident"])
            central_line(model, X_116, X_133, 116, 133, incident=True)
            return promote_point_to_top(model, X_2822)


        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_2822 on the given reference triangle."""
            model = create_model('X_2822 = ISOGONAL CONJUGATE OF X_2738')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02822(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-02822.json"))
            write_center_svg(
                model_acute,
                here / "x-02822.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2822¶

X₂₈₂₂¶