G.11 center of a circle — Code

I.def.16

The point A within the circle ( A B ) from which all segments / A B /, / A C / to the arc are equal is called the center of the circle.
A B C 
"""Programmatic construction for Book I, Definition 16 (I.def.16 — center of a circle).

        This point is called the center of the circle.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the foundational figure for I.def.16 (center A of circle ( B C D ))."""
            model = Model("I.def.16")
            A = model.set_point(0, 0, classes=["given"], ID="A")
            B = model.set_point(1, 0, classes=["given"], ID="B")
            model.construct_circle(A, B)
            C = model.set_point(sp.Rational(1, 2), sp.sqrt(3) / 2, ID="C")
            model.set_segment(A, B)
            model.set_segment(A, C)
            return model


        if __name__ == "__main__":
            construct_g1()