← etc / Encyclopedia of Triangle Centers

X₇₃₉¶

EVEN (- 1, 0) CIRCUMCIRCLE POINT

X₇₃₉ (EVEN (- 1, 0) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_739 = EVEN (- 1, 0) 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_barycentric_point,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00739(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_536 = eval_barycentric_point(model, A, B, C, '2*b*c - c*a - a*b', ID="X_536", classes=["center"])
            X_739 = isogonal_conjugate(model, A, B, C, X_536, ID="X_739", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_6, X_100, 6, 100, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", 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_31, X_101, 31, 101, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", 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_81, X_99, 81, 99, incident=True)
            return promote_point_to_top(model, X_739)


        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_739 on the given reference triangle."""
            model = create_model('X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00739(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-00739.json"))
            write_center_svg(
                model_acute,
                here / "x-00739.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X739¶

X₇₃₉¶