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X₃₈₁₄¶

X₂₀₇₇com(EULER TRIANGLE)

X₃₈₁₄ = nine-point-circle-inverse of X₁₀

X₃₈₁₄ (X₂₀₇₇com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3814 = X_2077com(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,
            centroid_of,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03814(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3814 = X_2077com(EULER TRIANGLE) on reference triangle ABC."""
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center"])
            X_3814 = complement(model, A, B, C, X_36, ID="X_3814", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            central_line(model, X_5, X_10, 5, 10, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_36, 2, 36, incident=True)
            X_119 = eval_trilinear_point(model, A, B, C, '(csc(A))*(-1 + cos(B) + cos(C))*(sin(2*B) + sin(2*C) + 2*(-1 + cos(A))*(sin(B) + sin(C)))', ID="X_119", 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_119, X_214, 119, 214, incident=True)
            return promote_point_to_top(model, X_3814)


        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_3814 on the given reference triangle."""
            model = create_model('X_3814 = X_2077com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03814(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-03814.json"))
            write_center_svg(
                model_acute,
                here / "x-03814.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3814¶

X₃₈₁₄¶