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X₃₇₈₉¶

X₃₆₇₉com[INVERSE(nT(bc, c²))]

X₃₇₈₉ (X₃₆₇₉com[INVERSE(nT(bc, c²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3789 = X_3679com[INVERSE(nT(bc, c²))]."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03789(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3789 = X_3679com[INVERSE(nT(bc, c²))] on reference triangle ABC."""
            X_3789 = eval_barycentric_point(model, A, B, C, '(a*(a**(2) - a*b - a*c - 2*b*c)*(b**(2) + c**(2) + b*c))', ID="X_3789", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center", "incident"])
            central_line(model, X_2, X_210, 2, 210, incident=True)
            X_120 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a*b*c - (b + c)*(a**(2) + (b - c)**(2)))*(b**(2) + c**(2) - a*b -a*c)', ID="X_120", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_120, X_141, 120, 141, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_350 = eval_trilinear_point(model, A, B, C, '(a**(2) - b*c)*b**(2)*c**(2)', ID="X_350", classes=["center", "incident"])
            central_line(model, X_8, X_350, 8, 350, incident=True)
            return promote_point_to_top(model, X_3789)


        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_3789 on the given reference triangle."""
            model = create_model('X_3789 = X_3679com[INVERSE(nT(bc, c²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03789(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-03789.json"))
            write_center_svg(
                model_acute,
                here / "x-03789.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3789¶

X₃₇₈₉¶