← etc / Encyclopedia of Triangle Centers

X₉₅₇¶

ISOGONAL CONJUGATE OF X₉₅₆

X₉₅₇ (ISOGONAL CONJUGATE OF X₉₅₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_957 = ISOGONAL CONJUGATE OF X_956."""

        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,
            centroid_of,
            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_00957(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_957 = ISOGONAL CONJUGATE OF X_956 on reference triangle ABC."""
            X_956 = eval_trilinear_point(model, A, B, C, '(a**(3) - a*(b - c)**(2) - 2*b*c*(b + c))', ID="X_956", classes=["center"])
            X_957 = isogonal_conjugate(model, A, B, C, X_956, ID="X_957", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_392 = eval_trilinear_point(model, A, B, C, '(b + c)*(b**(2) + c**(2) - a**(2)) + 4*a*b*c', ID="X_392", classes=["center", "incident"])
            central_line(model, X_2, X_392, 2, 392, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_859 = eval_trilinear_point(model, A, B, C, '((sin(A) + sin(B))*sin(2*B)*sin(C - A) + (sin(A) + sin(C))*sin(2*C)*sin(B - A))', ID="X_859", classes=["center", "incident"])
            central_line(model, X_81, X_859, 81, 859, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_995 = eval_trilinear_point(model, A, B, C, 'a*(a*b + a*c - b*c + b**(2) + c**(2))', ID="X_995", classes=["center", "incident"])
            central_line(model, X_57, X_995, 57, 995, incident=True)
            return promote_point_to_top(model, X_957)


        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_957 on the given reference triangle."""
            model = create_model('X_957 = ISOGONAL CONJUGATE OF X_956')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00957(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-00957.json"))
            write_center_svg(
                model_acute,
                here / "x-00957.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X957¶

X₉₅₇¶