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X₁₆₄₈¶

TRIPOLAR CENTROID OF X₅₂₃

X₁₆₄₈ is the tripolar centroid of X₅₂₃.

X₁₆₄₈ (TRIPOLAR CENTROID OF X₅₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1648 = TRIPOLAR CENTROID OF X_523."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01648(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1648 = TRIPOLAR CENTROID OF X_523 on reference triangle ABC."""
            X_1641 = point_from_barycentrics(model, A, B, C, -1.6171171, 0.22187902, 2.3952381, ID="X_1641", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1648 = reflection_in_point(model, X_1641, X_2, ID="X_1648", classes=["selected", "target"], guide=False)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_125 = eval_trilinear_point(model, A, B, C, 'cos(A)*(sin(B - C))**(2)', ID="X_125", classes=["center", "incident"])
            central_line(model, X_115, X_125, 115, 125, incident=True)
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center", "incident"])
            X_865 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*(csc(C))**(2)*sin(C - A)*csc(A - B) - sin(2*C)*(csc(B))**(2)*sin(B - A)*csc(A - C))', ID="X_865", classes=["center", "incident"])
            central_line(model, X_669, X_865, 669, 865, incident=True)
            return promote_point_to_top(model, X_1648)


        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_1648 on the given reference triangle."""
            model = create_model('X_1648 = TRIPOLAR CENTROID OF X_523')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01648(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-01648.json"))
            write_center_svg(
                model_acute,
                here / "x-01648.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1648¶

X₁₆₄₈¶