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X₈₃₁¶

o-(1, 3) CIRCUMCIRCLE POINT

X₈₃₁ (o-(1, 3) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_831 = o-(1, 3) 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_00831(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_831 = o-(1, 3) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_830 = eval_trilinear_point(model, A, B, C, '(a**(0)*(b**(3) - c**(3)) + a**(2)*(b**(1) - c**(1)))', ID="X_830", classes=["center"])
            X_831 = isogonal_conjugate(model, A, B, C, X_830, ID="X_831", classes=["selected", "target"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            X_827 = eval_trilinear_point(model, A, B, C, '1/(a**(-1)*(b**(4) - c**(4)) + a**(3)*(b**(0) - c**(0)))', ID="X_827", classes=["center", "incident"])
            central_line(model, X_662, X_827, 662, 827, incident=True)
            return promote_point_to_top(model, X_831)


        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_831 on the given reference triangle."""
            model = create_model('X_831 = o-(1, 3) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00831(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-00831.json"))
            write_center_svg(
                model_acute,
                here / "x-00831.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X831¶

X₈₃₁¶