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X₅₅₆¶

(X₁,X₇₅)-ANSWER TO QUESTION A

X₅₅₆ ((X₁,X₇₅)-ANSWER TO QUESTION A) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_556 = (X_1,X_75)-ANSWER TO QUESTION A."""

        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,
            isotomic_conjugate,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00556(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_556 = (X_1,X_75)-ANSWER TO QUESTION A on reference triangle ABC."""
            X_174 = eval_trilinear_point(model, A, B, C, 'sec(A/2)', ID="X_174", classes=["center"])
            X_556 = isotomic_conjugate(model, A, B, C, X_174, ID="X_556", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_177 = eval_trilinear_point(model, A, B, C, '(cos(B/2) + cos(C/2))*sec(A/2)', ID="X_177", classes=["center", "incident"])
            central_line(model, X_8, X_177, 8, 177, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_234 = eval_trilinear_point(model, A, B, C, '((cos(B/2) + cos(C/2))*(cos(B/2)*cos(C/2))**(2))', ID="X_234", classes=["center", "incident"])
            central_line(model, X_75, X_234, 75, 234, incident=True)
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            X_2090 = eval_trilinear_point(model, A, B, C, '((sin(B/2) + sin(C/2))*csc(A))', ID="X_2090", classes=["center", "incident"])
            central_line(model, X_312, X_2090, 312, 2090, incident=True)
            return promote_point_to_top(model, X_556)


        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_556 on the given reference triangle."""
            model = create_model('X_556 = (X_1,X_75)-ANSWER TO QUESTION A')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00556(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-00556.json"))
            write_center_svg(
                model_acute,
                here / "x-00556.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X556¶

X₅₅₆¶