← etc / Encyclopedia of Triangle Centers

X₁₆₄₉¶

TRIPOLAR CENTROID OF X₅₂₄

X₁₆₄₉ is the tripolar centroid of X₅₂₄.

X₁₆₄₉ (TRIPOLAR CENTROID OF X₅₂₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1649 = TRIPOLAR CENTROID OF X_524."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01649(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1649 = TRIPOLAR CENTROID OF X_524 on reference triangle ABC."""
            X_1649 = eval_barycentric_point(model, A, B, C, '(2*a**(2) - b**(2) - c**(2))**(2)*(b**(2) - c**(2))', ID="X_1649", classes=["selected", "target"])
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            X_126 = eval_trilinear_point(model, A, B, C, '(b*c*(2*a**(2) - b**(2) - c**(2))*(b**(4) + c**(4) + a**(2)*(b**(2) + c**(2)) - 4*b**(2)*c**(2)))', ID="X_126", classes=["center", "incident"])
            central_line(model, X_114, X_126, 114, 126, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_2, X_523, 2, 523, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center", "incident"])
            central_line(model, X_3, X_669, 3, 669, incident=True)
            return promote_point_to_top(model, X_1649)


        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_1649 on the given reference triangle."""
            model = create_model('X_1649 = TRIPOLAR CENTROID OF X_524')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01649(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-01649.json"))
            write_center_svg(
                model_acute,
                here / "x-01649.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1649¶

X₁₆₄₉¶