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X₁₆₃₈¶

TRIPOLAR CENTROID OF X₇

X₁₆₃₈ is the tripolar centroid of X₇.

X₁₆₃₈ (TRIPOLAR CENTROID OF X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1638 = TRIPOLAR CENTROID OF X_7."""

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


        def construct_x_01638(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1638 = TRIPOLAR CENTROID OF X_7 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=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_11, X_244, 11, 244, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", 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_57, X_654, 57, 654, 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_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            central_line(model, X_241, X_514, 241, 514, incident=True)
            return promote_point_to_top(model, X_1638)


        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_1638 on the given reference triangle."""
            model = create_model('X_1638 = TRIPOLAR CENTROID OF X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01638(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-01638.json"))
            write_center_svg(
                model_acute,
                here / "x-01638.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1638¶

X₁₆₃₈¶