hamlet over hears the plotting palonius, claudius, and his mother. what is result?

Polonius tells the king and queen, in a very roundabout way, that he has discovered Hamlet’s foiled love of Ophelia, and that he believes this lost love to be the root cause of Hamlet’s madness. Claudius asks how they might prove this to be the case. Polonius has a plan. He offers to loose Ophelia on Hamlet while he is reading alone in the library. Meanwhile, he suggests, he and Claudius could hide behind a tapestry and observe the meeting. Claudius agrees.

Just then, Hamlet enters, reading. Gertrude and Claudius exit while Polonius attempts to speak to Hamlet. Hamlet plays with Polonius, mocking him, evading his questions, and turning his language inside out. Nevertheless, Polonius “reads between the lines,” as it were, and interprets Hamlet’s nonsensical replies as motivated by a broken heart. Polonius leaves to contrive the proposed meeting between Hamlet and his daughter.