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X₃₅₆₅¶

2nd MOSES CIRCUMCIRCLE POINT

X₃₅₆₅ = reflection of X₃₅₆₃ in X₃

X₃₅₆₅ (2nd MOSES CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3565 = 2nd MOSES 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03565(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3565 = 2nd MOSES CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_3563 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b**(2)*(cos(C))**(2) + c**(2)*(cos(B))**(2) - b*c*cos(A))', ID="X_3563", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_3565 = reflection_in_point(model, X_3563, X_3, ID="X_3565", classes=["selected", "target"], guide=False)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_20, X_98, 20, 98, incident=True)
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_22, X_111, 22, 111, incident=True)
            X_376 = eval_trilinear_point(model, A, B, C, '5*cos(A) - cos(B - C)', ID="X_376", classes=["center", "incident"])
            X_1300 = eval_trilinear_point(model, A, B, C, '(sec(A))/(1 + cos(2*B) + cos(2*C))', ID="X_1300", classes=["center", "incident"])
            central_line(model, X_376, X_1300, 376, 1300, incident=True)
            return promote_point_to_top(model, X_3565)


        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_3565 on the given reference triangle."""
            model = create_model('X_3565 = 2nd MOSES CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03565(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-03565.json"))
            write_center_svg(
                model_acute,
                here / "x-03565.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3565¶

X₃₅₆₅¶