Final answer:
The Java GUI library to place a letter on a board game using a radio button is the Swing Library.
Step-by-step explanation:
The subject of this question is Computers and Technology. The question is asking about the Java GUI library that can be used to place a letter on a board game using a radio button. The correct answer is A. Swing Library. This library is part of the Java Foundation Classes (JFC) and provides a set of components and classes for building graphical user interfaces in Java.