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X₁₆₄₂¶

TRIPOLAR CENTROID OF X₁₀₀

X₁₆₄₂ is the tripolar centroid of X₁₀₀.

X₁₆₄₂ (TRIPOLAR CENTROID OF X₁₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1642 = TRIPOLAR CENTROID OF X_100."""

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


        def construct_x_01642(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1642 = TRIPOLAR CENTROID OF X_100 on reference triangle ABC."""
            X_1642 = eval_trilinear_point(model, A, B, C, '(a*b + a*c - b**(2) - c**(2))*(2*a**(3) - 2*a**(2)*(b + c) + a*(b**(2) + c**(2)) - (b - c)**(2)*(b + c))', ID="X_1642", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_241 = eval_trilinear_point(model, A, B, C, '(cos(B/2))**(4) - ((cos(A/2))**(2))*((cos(B/2))**(2) +(cos(C/2))**(2)) + (cos(C/2))**(4)', ID="X_241", classes=["center", "incident"])
            X_1025 = eval_trilinear_point(model, A, B, C, '((b**(2) + c**(2) - a*(b + c))/((b - c)*(b + c - a)))', ID="X_1025", classes=["center", "incident"])
            central_line(model, X_241, X_1025, 241, 1025, incident=True)
            return promote_point_to_top(model, X_1642)


        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_1642 on the given reference triangle."""
            model = create_model('X_1642 = TRIPOLAR CENTROID OF X_100')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01642(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-01642.json"))
            write_center_svg(
                model_acute,
                here / "x-01642.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1642¶

X₁₆₄₂¶