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X₃₈₇₄¶

X₁₄₀com[INVERSE(n(3rd EULER TRIANGLE))]

X₃₈₇₄ = complement of X₅₉₀₄

X₃₈₇₄ (X₁₄₀com[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_3874 = X_140com[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,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03874(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3874 = X_140com[INVERSE(n(3rd EULER TRIANGLE))] on reference triangle ABC."""
            X_3874 = eval_barycentric_point(model, A, B, C, '(a*(b**(3) + c**(3) - a**(2)*b - a**(2)*c - 2*a*b*c))', ID="X_3874", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_1, X_21, 1, 21, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", 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_10, X_141, 10, 141, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_214 = eval_trilinear_point(model, A, B, C, '(b + c - 2*a)*(b**(2) + c**(2) - a**(2) - b*c)', ID="X_214", classes=["center", "incident"])
            central_line(model, X_56, X_214, 56, 214, incident=True)
            return promote_point_to_top(model, X_3874)


        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_3874 on the given reference triangle."""
            model = create_model('X_3874 = X_140com[INVERSE(n(3rd EULER TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03874(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-03874.json"))
            write_center_svg(
                model_acute,
                here / "x-03874.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3874¶

X₃₈₇₄¶