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X₂₀₅₀¶

{X₃,X₅}-HARMONIC CONJUGATE OF X₂₀₄₉

X₂₀₅₀ is the {X₃,X₅}-harmonic conjugate of X₂₀₄₉.

X₂₀₅₀ ({X₃,X₅}-HARMONIC CONJUGATE OF X₂₀₄₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2050 = {X_3,X_5}-HARMONIC CONJUGATE OF X_2049."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02050(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2050 = {X_3,X_5}-HARMONIC CONJUGATE OF X_2049 on reference triangle ABC."""
            X_2050 = eval_trilinear_point(model, A, B, C, '((s**(2) - r**(2))*cos(A) - (s**(2) + r**(2))*cos(B - C))', ID="X_2050", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_1460 = point_from_barycentrics(model, A, B, C, 0.16086235, 0.28656716, 0.55257048, ID="X_1460", classes=["center", "incident"])
            central_line(model, X_11, X_1460, 11, 1460, incident=True)
            X_171 = eval_trilinear_point(model, A, B, C, 'a**(2) + b*c', ID="X_171", classes=["center", "incident"])
            X_1699 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A) + cos(B) + cos(C) - 1', ID="X_1699", classes=["center", "incident"])
            central_line(model, X_171, X_1699, 171, 1699, incident=True)
            return promote_point_to_top(model, X_2050)


        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_2050 on the given reference triangle."""
            model = create_model('X_2050 = {X_3,X_5}-HARMONIC CONJUGATE OF X_2049')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02050(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-02050.json"))
            write_center_svg(
                model_acute,
                here / "x-02050.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2050¶

X₂₀₅₀¶