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X₃₆₅₃¶

CENTROID OF {X₁, X₂, X₃}

X₃₆₅₃ is the centroid of {X₁, X₂, X₃}.

X₃₆₅₃ (CENTROID OF {X₁, X₂, X₃}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3653 = CENTROID OF {X_1, X_2, X_3}."""

        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_trilinear_point,
            incenter_of,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03653(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3653 = CENTROID OF {X_1, X_2, X_3} on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_355 = eval_trilinear_point(model, A, B, C, 'a*cos(A) - (b + c)*cos(B - C)', ID="X_355", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_549 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 4*cos(A)', ID="X_549", classes=["center"])
            central_line(model, X_2, X_355, 2, 355)
            central_line(model, X_1, X_549, 1, 549)
            X_3653 = intersect_lines(model, X_2, X_355, X_1, X_549, ID="X_3653", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_551 = eval_trilinear_point(model, A, B, C, '(4*a + b + c)/a', ID="X_551", classes=["center", "incident"])
            central_line(model, X_3, X_551, 3, 551, incident=True)
            return promote_point_to_top(model, X_3653)


        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_3653 on the given reference triangle."""
            model = create_model('X_3653 = CENTROID OF {X_1, X_2, X_3}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03653(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-03653.json"))
            write_center_svg(
                model_acute,
                here / "x-03653.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3653¶

X₃₆₅₃¶