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X₁₆₃₉¶

TRIPOLAR CENTROID OF X₈

X₁₆₃₉ is the tripolar centroid of X₈.

X₁₆₃₉ (TRIPOLAR CENTROID OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1639 = TRIPOLAR CENTROID OF X_8."""

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


        def construct_x_01639(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1639 = TRIPOLAR CENTROID OF X_8 on reference triangle ABC."""
            X_1638 = eval_barycentric_point(model, A, B, C, '(b - c)*(2*a**(2) - b**(2) - c**(2) - a*b - a*c + 2*b*c)', ID="X_1638", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1639 = reflection_in_point(model, X_1638, X_2, ID="X_1639", classes=["selected", "target"], guide=False)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_654 = eval_trilinear_point(model, A, B, C, 'cos(A - B) - cos(C - A)', ID="X_654", classes=["center", "incident"])
            central_line(model, X_9, X_654, 9, 654, incident=True)
            X_918 = eval_barycentric_point(model, A, B, C, '((b - c)*(b**(2) + c**(2) -a*b - a*c))', ID="X_918", classes=["center", "incident"])
            central_line(model, X_2, X_918, 2, 918, incident=True)
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center", "incident"])
            X_926 = eval_trilinear_point(model, A, B, C, 'a*(a - b - c)*(b - c)*(a*b + a*c - b**(2) - c**(2))', ID="X_926", classes=["center", "incident"])
            central_line(model, X_210, X_926, 210, 926, incident=True)
            return promote_point_to_top(model, X_1639)


        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_1639 on the given reference triangle."""
            model = create_model('X_1639 = TRIPOLAR CENTROID OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01639(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-01639.json"))
            write_center_svg(
                model_acute,
                here / "x-01639.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1639¶

X₁₆₃₉¶