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X₃₇₈₀¶

X₃₇₂₁com[T(-bc, b²)]

X₃₇₈₀ (X₃₇₂₁com[T(-bc, b²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3780 = X_3721com[T(-bc, b²)]."""

        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,
            nagel_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03780(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3780 = X_3721com[T(-bc, b²)] on reference triangle ABC."""
            X_3780 = eval_barycentric_point(model, A, B, C, '(a*(a**(2)*b + a**(2)*c + 2*a*b*c - b**(2)*c - b*c**(2)))', ID="X_3780", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_6, X_8, 6, 8, incident=True)
            X_213 = eval_trilinear_point(model, A, B, C, '(b + c)*a**(2)', ID="X_213", classes=["center", "incident"])
            X_519 = eval_trilinear_point(model, A, B, C, '(2*a - b - c)/a', ID="X_519", classes=["center", "incident"])
            central_line(model, X_213, X_519, 213, 519, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_1107 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2)) + b*c*(b + c))', ID="X_1107", classes=["center", "incident"])
            central_line(model, X_42, X_1107, 42, 1107, incident=True)
            return promote_point_to_top(model, X_3780)


        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_3780 on the given reference triangle."""
            model = create_model('X_3780 = X_3721com[T(-bc, b²)]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03780(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-03780.json"))
            write_center_svg(
                model_acute,
                here / "x-03780.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3780¶

X₃₇₈₀¶