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X₃₈₉₁¶

X₂₈₈₇com[INVERSE(n(3rd EULER TRIANGLE))]

X₃₈₉₁ (X₂₈₈₇com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3891 = X_2887com[INVERSE(n(3rd EULER TRIANGLE))]."""

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


        def construct_x_03891(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3891 = X_2887com[INVERSE(n(3rd EULER TRIANGLE))] on reference triangle ABC."""
            X_3891 = eval_barycentric_point(model, A, B, C, '(a**(3) + a*b**(2) + a*c**(2) - b**(2)*c - b*c**(2))', ID="X_3891", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_1, X_321, 1, 321, incident=True)
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            X_388 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) + (b + c)**(2))/(b + c - a)', ID="X_388", classes=["center", "incident"])
            central_line(model, X_145, X_388, 145, 388, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_726 = eval_trilinear_point(model, A, B, C, '(a **(-3)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-2) + c **(-2)))', ID="X_726", classes=["center", "incident"])
            central_line(model, X_31, X_726, 31, 726, incident=True)
            return promote_point_to_top(model, X_3891)


        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_3891 on the given reference triangle."""
            model = create_model('X_3891 = X_2887com[INVERSE(n(3rd EULER TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03891(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-03891.json"))
            write_center_svg(
                model_acute,
                here / "x-03891.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3891¶

X₃₈₉₁¶