← etc / Encyclopedia of Triangle Centers

X₇₂₇¶

EVEN (- 2, -1) CIRCUMCIRCLE POINT

X₇₂₇ (EVEN (- 2, -1) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT."""

        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_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00727(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_726 = eval_trilinear_point(model, A, B, C, '(a **(-3)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-2) + c **(-2)))', ID="X_726", classes=["center"])
            X_727 = isogonal_conjugate(model, A, B, C, X_726, ID="X_727", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            central_line(model, X_31, X_43, 31, 43, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_32, X_101, 32, 101, incident=True)
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_58, X_99, 58, 99, incident=True)
            return promote_point_to_top(model, X_727)


        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_727 on the given reference triangle."""
            model = create_model('X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00727(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-00727.json"))
            write_center_svg(
                model_acute,
                here / "x-00727.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X727¶

X₇₂₇¶