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X₈₆₆¶

INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X₅₁₃

X₈₆₆ = crossdifference of every pair of points on line X₁₀₀ X₆₄₇

X₈₆₆ (INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X₅₁₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_866 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_513."""

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


        def construct_x_00866(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_866 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_513 on reference triangle ABC."""
            X_866 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(A - C)/(sin(A) - sin(B)) - sin(2*C)*sin(A - B)/(sin(A) - sin(C)))', ID="X_866", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            central_line(model, X_244, X_665, 244, 665, incident=True)
            return promote_point_to_top(model, X_866)


        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_866 on the given reference triangle."""
            model = create_model('X_866 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X_513')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00866(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-00866.json"))
            write_center_svg(
                model_acute,
                here / "x-00866.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X866¶

X₈₆₆¶