← etc / Encyclopedia of Triangle Centers

X₉₃₇¶

ISOGONAL CONJUGATE OF X₉₃₆

X₉₃₇ (ISOGONAL CONJUGATE OF X₉₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_937 = ISOGONAL CONJUGATE OF X_936."""

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


        def construct_x_00937(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_937 = ISOGONAL CONJUGATE OF X_936 on reference triangle ABC."""
            X_936 = eval_trilinear_point(model, A, B, C, 'a**(3) - a**(2)*(b + c) - a*(b - c)**(2) + (b + c)**(3)', ID="X_936", classes=["center"])
            X_937 = isogonal_conjugate(model, A, B, C, X_936, ID="X_937", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            central_line(model, X_6, X_40, 6, 40, incident=True)
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            X_196 = eval_trilinear_point(model, A, B, C, '((cos(B) + cos(C) - cos(A) - 1)*sec(A)*tan(A/2))', ID="X_196", classes=["center", "incident"])
            central_line(model, X_34, X_196, 34, 196, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_223 = eval_trilinear_point(model, A, B, C, '(tan(A/2))*(cos(B) + cos(C) - cos(A) - 1)', ID="X_223", classes=["center", "incident"])
            central_line(model, X_56, X_223, 56, 223, incident=True)
            return promote_point_to_top(model, X_937)


        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_937 on the given reference triangle."""
            model = create_model('X_937 = ISOGONAL CONJUGATE OF X_936')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00937(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-00937.json"))
            write_center_svg(
                model_acute,
                here / "x-00937.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X937¶

X₉₃₇¶