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X₈₁₃¶

o-(- 1, 1) CIRCUMCIRCLE POINT

X₈₁₃ (o-(- 1, 1) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_813 = o-(- 1, 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_00813(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_812 = eval_trilinear_point(model, A, B, C, 'a **(-2)*(b**(1) - c**(1)) + a**(0)*(b **(-1) - c **(-1))', ID="X_812", classes=["center"])
            X_813 = isogonal_conjugate(model, A, B, C, X_812, ID="X_813", classes=["selected", "target"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            central_line(model, X_105, X_238, 105, 238, incident=True)
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            X_295 = eval_trilinear_point(model, A, B, C, '(cos(A))/(a**(2) - b*c)', ID="X_295", classes=["center", "incident"])
            central_line(model, X_103, X_295, 103, 295, incident=True)
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            X_292 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) - b*c)', ID="X_292", classes=["center", "incident"])
            central_line(model, X_106, X_292, 106, 292, incident=True)
            return promote_point_to_top(model, X_813)


        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_813 on the given reference triangle."""
            model = create_model('X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00813(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-00813.json"))
            write_center_svg(
                model_acute,
                here / "x-00813.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X813¶

X₈₁₃¶