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X₃₀₂₀¶

4th STEVANOVIC POINT

Centers X₃₀₂₀-X₃₀₂₆ are points on the incircle, as noted by Milorad Stevanovic (Hyacinthos, Dec. 7-8, 2004)

X₃₀₂₀ (4th STEVANOVIC POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3020 = 4th STEVANOVIC POINT."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03020(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3020 = 4th STEVANOVIC POINT on reference triangle ABC."""
            X_3020 = eval_barycentric_point(model, A, B, C, '((b + c - a)*((b - c)*(b**(2) + c**(2) - b*c))**(2))', ID="X_3020", classes=["selected", "target"])
            X_1086 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)**(2))', ID="X_1086", classes=["center", "incident"])
            X_3023 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a)*(b - c)**(2)*(a**(2) + b*c)**(2))', ID="X_3023", classes=["center", "incident"])
            central_line(model, X_1086, X_3023, 1086, 3023, incident=True)
            return promote_point_to_top(model, X_3020)


        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_3020 on the given reference triangle."""
            model = create_model('X_3020 = 4th STEVANOVIC POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03020(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-03020.json"))
            write_center_svg(
                model_acute,
                here / "x-03020.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3020¶

X₃₀₂₀¶