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X₂₉₅₉¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₁₄₇

X₂₉₅₉ is the excentral-isogonal conjugate of X₁₄₇.

X₂₉₅₉ (EXCENTRAL-ISOGONAL CONJUGATE OF X₁₄₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2959 = EXCENTRAL-ISOGONAL CONJUGATE OF X_147."""

        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,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02959(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2959 = EXCENTRAL-ISOGONAL CONJUGATE OF X_147 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1326 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) - a**(2) + b*c - a*b - a*c)/(b + c))', ID="X_1326", classes=["center"])
            X_2959 = reflection_in_point(model, X_1, X_1326, ID="X_2959", classes=["selected", "target"], guide=False)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", 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_40, X_511, 40, 511, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_1247 = point_from_barycentrics(model, A, B, C, 0.47979502, 0.29838347, 0.22182151, ID="X_1247", classes=["center", "incident"])
            central_line(model, X_19, X_1247, 19, 1247, incident=True)
            central_line(model, X_1, X_1326, 1, 1326, incident=True)
            return promote_point_to_top(model, X_2959)


        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_2959 on the given reference triangle."""
            model = create_model('X_2959 = EXCENTRAL-ISOGONAL CONJUGATE OF X_147')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02959(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-02959.json"))
            write_center_svg(
                model_acute,
                here / "x-02959.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2959¶

X₂₉₅₉¶