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X₆₁₆¶

ANTICOMPLEMENT OF X₁₃

The midpoint of X₆₁₆ and X₆₁₇ is the Steiner point, X₉₉.

X₆₁₆ (ANTICOMPLEMENT OF X₁₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_616 = ANTICOMPLEMENT OF X_13."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00616(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_616 = ANTICOMPLEMENT OF X_13 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center"])
            central_line(model, X_2, X_13, 2, 13)
            central_line(model, X_69, X_74, 69, 74)
            X_616 = intersect_lines(model, X_2, X_13, X_69, X_74, ID="X_616", classes=["selected", "target"])
            X_14 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /3)', ID="X_14", classes=["center", "incident"])
            X_148 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - (b**(2) - c**(2))**(2) + b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_148", classes=["center", "incident"])
            central_line(model, X_14, X_148, 14, 148, incident=True)
            return promote_point_to_top(model, X_616)


        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_616 on the given reference triangle."""
            model = create_model('X_616 = ANTICOMPLEMENT OF X_13')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00616(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-00616.json"))
            write_center_svg(
                model_acute,
                here / "x-00616.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X616¶

X₆₁₆¶