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X₂₇₇₆¶

ISOGONAL CONJUGATE OF X₂₆₉₂

As the isogonal conjugate of a point on the circumcircle, X₂₇₇₆ lies on the line at infinity.

X₂₇₇₆ (ISOGONAL CONJUGATE OF X₂₆₉₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2776 = ISOGONAL CONJUGATE OF X_2692."""

        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_02776(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2776 = ISOGONAL CONJUGATE OF X_2692 on reference triangle ABC."""
            X_2692 = point_from_barycentrics(model, A, B, C, 0.15981192, 1.0991936, -0.25900548, ID="X_2692", classes=["center"])
            X_2776 = isogonal_conjugate(model, A, B, C, X_2692, ID="X_2776", classes=["selected", "target"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            central_line(model, X_74, X_106, 74, 106, incident=True)
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            X_121 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - 2*a)*(b**(3) + c**(3) + a*(b**(2) + c**(2)) - 2*b*c*(b + c)))', ID="X_121", classes=["center", "incident"])
            central_line(model, X_113, X_121, 113, 121, 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_2776)


        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_2776 on the given reference triangle."""
            model = create_model('X_2776 = ISOGONAL CONJUGATE OF X_2692')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02776(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-02776.json"))
            write_center_svg(
                model_acute,
                here / "x-02776.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2776¶

X₂₇₇₆¶