Problem
1979 AHSME Problem 17
![[asy] size(200); dotfactor=3; pair A=(0,0),B=(1,0),C=(2,0),D=(3,0),X=(1.2,0.7); draw(A--D); dot(A);dot(B);dot(C);dot(D); draw(arc((0.4,0.4),0.4,180,110),arrow = Arrow(TeXHead)); draw(arc((2.6,0.4),0.4,0,70),arrow = Arrow(TeXHead)); draw(B--X,dotted); draw(C--X,dotted); label("$A$",A,SW); label("$B$",B,S); label("$C$",C,S); label("$D$",D,S); label("x",X,fontsize(5pt)); //Credit to TheMaskedMagician for the diagram [/asy]](/static/aops/78eb32a52b6716abe7e8df0c92b9c4691fc0e2af.png)
Points A , B, C, and D are distinct and lie, in the given order, on a straight line. Line segments AB, AC, and AD have lengths x, y, and z, respectively. If line segments AB and CD may be rotated about points B and C, respectively, so that points A and D coincide, to form a triangle with positive area, then which of the following three inequalities must be satisfied?
\begin{array}{l} \textbf{I. }x<\frac{z}{2}\qquad\\ \textbf{II. }y<x+\frac{z}{2}\qquad\\ \textbf{III. }y<\frac{z}{2}\qquad \end{array}
\textbf{(A) }\textbf{I. }\text{only}\qquad \textbf{(B) }\textbf{II. }\text{only}\qquad \textbf{(C) }\textbf{I. }\text{and }\textbf{II. }\text{only}\qquad \textbf{(D) }\textbf{II. }\text{and }\textbf{III. }\text{only}\qquad \textbf{(E) }\textbf{I. },\textbf{II. },\text{and }\textbf{III. }
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