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X₂₄₂₂¶

ISOGONAL CONJUGATE OF X₂₃₉₆

X₂₄₂₂ is the isogonal conjugate of X₂₃₉₆.

X₂₄₂₂ (ISOGONAL CONJUGATE OF X₂₃₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2422 = ISOGONAL CONJUGATE OF X_2396."""

        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_barycentric_point,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02422(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2422 = ISOGONAL CONJUGATE OF X_2396 on reference triangle ABC."""
            X_2396 = eval_barycentric_point(model, A, B, C, '(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2))/(b**(2) - c**(2))', ID="X_2396", classes=["center"])
            X_2422 = isogonal_conjugate(model, A, B, C, X_2396, ID="X_2422", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_6, X_523, 6, 523, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_32, X_512, 32, 512, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_729 = eval_trilinear_point(model, A, B, C, '1/(a**(-3)*(b**(0) + c**(0)) - a **(-1)*(b**(-2) + c **(-2)))', ID="X_729", classes=["center", "incident"])
            central_line(model, X_98, X_729, 98, 729, incident=True)
            return promote_point_to_top(model, X_2422)


        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_2422 on the given reference triangle."""
            model = create_model('X_2422 = ISOGONAL CONJUGATE OF X_2396')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02422(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-02422.json"))
            write_center_svg(
                model_acute,
                here / "x-02422.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2422¶

X₂₄₂₂¶