1953 AHSME Problem 14

Given the larger of two circles with center P and radius p and the smaller with center Q and radius q. Draw PQ. Which of the following statements is false?

\begin{array}{l} \textbf{(A)}\ p-q\text{ can be equal to }\overline{PQ}\\ \textbf{(B)}\ p+q\text{ can be equal to }\overline{PQ}\\ \textbf{(C)}\ p+q\text{ can be less than }\overline{PQ}\\ \textbf{(D)}\ p-q\text{ can be less than }\overline{PQ}\\ \textbf{(E)}\ \text{none of these} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.