← etc / Encyclopedia of Triangle Centers

X₆₉₉¶

EVEN (- 4, - 2) CIRCUMCIRCLE POINT

X₆₉₉ (EVEN (- 4, - 2) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_699 = EVEN (- 4, - 2) 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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00699(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_698 = eval_trilinear_point(model, A, B, C, '(a **(-5)*(b **(-2) + c **(-2)) - a **(-3)*(b **(-4) + c **(-4)))', ID="X_698", classes=["center"])
            X_699 = isogonal_conjugate(model, A, B, C, X_698, ID="X_699", classes=["selected", "target"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", 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_32, X_99, 32, 99, incident=True)
            X_251 = eval_trilinear_point(model, A, B, C, 'a**(2)*csc(A +  omega  )', ID="X_251", classes=["center", "incident"])
            X_689 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(4) - c**(4)))', ID="X_689", classes=["center", "incident"])
            central_line(model, X_251, X_689, 251, 689, incident=True)
            X_172 = eval_trilinear_point(model, A, B, C, 'a**(3) + a*b*c', ID="X_172", classes=["center", "incident"])
            X_932 = point_from_barycentrics(model, A, B, C, 0.76211763, -0.28424928, 0.52213165, ID="X_932", classes=["center", "incident"])
            central_line(model, X_172, X_932, 172, 932, incident=True)
            return promote_point_to_top(model, X_699)


        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_699 on the given reference triangle."""
            model = create_model('X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00699(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-00699.json"))
            write_center_svg(
                model_acute,
                here / "x-00699.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X699¶

X₆₉₉¶