← etc / Encyclopedia of Triangle Centers

X₅₂₇¶

DIRECTION OF VECTOR AX + BX + CX, where X = X₇

X₅₂₇ (DIRECTION OF VECTOR AX + BX + CX, where X = X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            gergonne_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00527(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X_7 on reference triangle ABC."""
            X_527 = eval_barycentric_point(model, A, B, C, '2*a**(2) - a*(b + c) - (b - c)**(2)', ID="X_527", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_2, X_7, 2, 7, incident=True)
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_320 = eval_trilinear_point(model, A, B, C, '(1 - 2*cos(A))/a**(2)', ID="X_320", classes=["center", "incident"])
            central_line(model, X_190, X_320, 190, 320, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            return promote_point_to_top(model, X_527)


        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_527 on the given reference triangle."""
            model = create_model('X_527 = DIRECTION OF VECTOR AX + BX + CX, where X = X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00527(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-00527.json"))
            write_center_svg(
                model_acute,
                here / "x-00527.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X527¶

X₅₂₇¶