← etc / Encyclopedia of Triangle Centers

X₂₈₂₄¶

ISOGONAL CONJUGATE OF X₂₇₄₀

X₂₈₂₄ is the isogonal conjugate of X₂₇₄₀.

X₂₈₂₄ (ISOGONAL CONJUGATE OF X₂₇₄₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2824 = ISOGONAL CONJUGATE OF X_2740."""

        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_02824(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2824 = ISOGONAL CONJUGATE OF X_2740 on reference triangle ABC."""
            X_2740 = point_from_barycentrics(model, A, B, C, 0.15630727, 1.0979341, -0.25424138, ID="X_2740", classes=["center"])
            X_2824 = isogonal_conjugate(model, A, B, C, X_2740, ID="X_2824", classes=["selected", "target"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_103, X_111, 103, 111, incident=True)
            X_118 = point_from_barycentrics(model, A, B, C, 0.28918651, -0.056547619, 0.76736111, ID="X_118", classes=["center", "incident"])
            X_126 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a**(2) - b**(2) - c**(2))*(b**(4) + c**(4) + a**(2)*(b**(2) + c**(2)) - 4*b**(2)*c**(2)))', ID="X_126", classes=["center", "incident"])
            central_line(model, X_118, X_126, 118, 126, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            return promote_point_to_top(model, X_2824)


        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_2824 on the given reference triangle."""
            model = create_model('X_2824 = ISOGONAL CONJUGATE OF X_2740')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02824(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-02824.json"))
            write_center_svg(
                model_acute,
                here / "x-02824.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2824¶

X₂₈₂₄¶