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X₁₅₇₀¶

MOSES-CIRCLE INVERSE OF X₃

X₁₅₇₀ is the moses-circle inverse of X₃.

X₁₅₇₀ (MOSES-CIRCLE INVERSE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1570 = MOSES-CIRCLE INVERSE OF X_3."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01570(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1570 = MOSES-CIRCLE INVERSE OF X_3 on reference triangle ABC."""
            X_1570 = eval_trilinear_point(model, A, B, C, 'a*(cot(A) + cot(omega)  - 4*tan(omega)  )', ID="X_1570", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_193 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cot(B) + cot(C) - cot(A))', ID="X_193", classes=["center", "incident"])
            X_625 = eval_trilinear_point(model, A, B, C, '(2*(b**(4) + c**(4) - b**(2)*c**(2)) - a**(2)*(b**(2) + c**(2)))/a', ID="X_625", classes=["center", "incident"])
            central_line(model, X_193, X_625, 193, 625, incident=True)
            return promote_point_to_top(model, X_1570)


        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_1570 on the given reference triangle."""
            model = create_model('X_1570 = MOSES-CIRCLE INVERSE OF X_3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01570(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-01570.json"))
            write_center_svg(
                model_acute,
                here / "x-01570.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1570¶

X₁₅₇₀¶