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X₂₉₄₆¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₁₆

X₂₉₄₆ is the excentral-isogonal conjugate of X₁₆.

X₂₉₄₆ (EXCENTRAL-ISOGONAL CONJUGATE OF X₁₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2946 = EXCENTRAL-ISOGONAL CONJUGATE OF X_16."""

        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,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02946(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2946 = EXCENTRAL-ISOGONAL CONJUGATE OF X_16 on reference triangle ABC."""
            X_15 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /3)', ID="X_15", classes=["center"])
            X_846 = eval_trilinear_point(model, A, B, C, '(- a**(2) + b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_846", classes=["center"])
            X_62 = eval_trilinear_point(model, A, B, C, 'sin(A -  pi  /6)', ID="X_62", classes=["center"])
            X_1046 = point_from_barycentrics(model, A, B, C, 0.13236391, 0.3064877, 0.5611484, ID="X_1046", classes=["center"])
            central_line(model, X_15, X_846, 15, 846)
            central_line(model, X_62, X_1046, 62, 1046)
            X_2946 = intersect_lines(model, X_15, X_846, X_62, X_1046, ID="X_2946", classes=["selected", "target"])
            X_573 = eval_trilinear_point(model, A, B, C, 'cos(A + U)', ID="X_573", classes=["center", "incident"])
            X_1761 = point_from_barycentrics(model, A, B, C, 0.54015296, 0.3957935, 0.064053537, ID="X_1761", classes=["center", "incident"])
            central_line(model, X_573, X_1761, 573, 1761, incident=True)
            return promote_point_to_top(model, X_2946)


        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_2946 on the given reference triangle."""
            model = create_model('X_2946 = EXCENTRAL-ISOGONAL CONJUGATE OF X_16')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02946(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-02946.json"))
            write_center_svg(
                model_acute,
                here / "x-02946.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2946¶

X₂₉₄₆¶