← etc / Encyclopedia of Triangle Centers

X₁₆₄₇¶

TRIPOLAR CENTROID OF X₅₁₄

X₁₆₄₇ is the tripolar centroid of X₅₁₄.

X₁₆₄₇ (TRIPOLAR CENTROID OF X₅₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1647 = TRIPOLAR CENTROID OF X_514."""

        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,
            feuerbach_point_of,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01647(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1647 = TRIPOLAR CENTROID OF X_514 on reference triangle ABC."""
            X_1644 = point_from_barycentrics(model, A, B, C, 0.70710678, 0, -0.70710678, ID="X_1644", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1647 = reflection_in_point(model, X_1644, X_2, ID="X_1647", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            central_line(model, X_80, X_106, 80, 106, incident=True)
            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)
            return promote_point_to_top(model, X_1647)


        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_1647 on the given reference triangle."""
            model = create_model('X_1647 = TRIPOLAR CENTROID OF X_514')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01647(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-01647.json"))
            write_center_svg(
                model_acute,
                here / "x-01647.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1647¶

X₁₆₄₇¶