← etc / Encyclopedia of Triangle Centers

X₈₃₉¶

o-(3, 4) CIRCUMCIRCLE POINT

X₈₃₉ (o-(3, 4) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_839 = o-(3, 4) 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_00839(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_839 = o-(3, 4) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_838 = eval_trilinear_point(model, A, B, C, '(a**(2)*(b**(4) - c**(4)) + a**(3)*(b**(3) - c**(3)))', ID="X_838", classes=["center"])
            X_839 = isogonal_conjugate(model, A, B, C, X_838, ID="X_839", classes=["selected", "target"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_668 = eval_trilinear_point(model, A, B, C, '1/(a**(2)*(b - c))', ID="X_668", classes=["center", "incident"])
            central_line(model, X_110, X_668, 110, 668, incident=True)
            X_334 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(a**(2) - b*c)', ID="X_334", classes=["center", "incident"])
            X_741 = eval_trilinear_point(model, A, B, C, '(1/(a **(-2)*(b**(1) + c**(1)) - a**(0)*(b **(-1) + c **(-1))))', ID="X_741", classes=["center", "incident"])
            central_line(model, X_334, X_741, 334, 741, incident=True)
            return promote_point_to_top(model, X_839)


        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_839 on the given reference triangle."""
            model = create_model('X_839 = o-(3, 4) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00839(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-00839.json"))
            write_center_svg(
                model_acute,
                here / "x-00839.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X839¶

X₈₃₉¶