G.145 converse of the tangent-secant theorem — Code

III.37

If from a point outside a circle a secant and a segment to the circle are drawn such that the rectangle on the whole secant and its external part equals the square on the segment, the segment is tangent to the circle.

"""Programmatic construction for Book III, Proposition 37 (III.37)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0082.g1 using geometor.model."""
            model = Model("III.37")

            # Circle ABC with center F(156, -84), radius 52 (y-inverted)
            F = model.set_point(156.0, -84.0, ID="F")
            E = model.set_point(156.0, -32.0, ID="E")
            D = model.set_point(24.0, -32.0, classes=["given"], ID="D")
            B = model.set_point(120.54, -122.02, classes=["given"], ID="B")
            C = model.set_point(104.08, -81.19, ID="C")
            A = model.set_point(181.97, -129.04, ID="A")

            # Circle ABC
            model.construct_circle(F, E)

            # Segments
            model.set_segment(D, E)
            model.set_segment(D, B)
            model.set_segment(A, D)
            model.set_segment(A, C)
            model.set_segment(C, D)
            model.set_segment(F, E)
            model.set_segment(F, B)
            model.set_segment(F, D)

            # Section
            model.set_section([D, C, A])

            # Polygons
            model.set_polygon([F, E, D])
            model.set_polygon([F, B, D])

            # Angles
            model.set_wedge(E, F, F, D)
            model.set_wedge(B, D, D, F)

            return model


        if __name__ == "__main__":
            construct_g1()