Answer: Odysseus convinces Penelope that he is Odysseus because c) only he would know the secret about the bed.
Explanation: When Odysseus returns to Ithaca disguised as a beggar, Penelope suspects that he is actually Odysseus but she is not completely sure about it. As a result, Penelope tests his identity by asking Eurycleia to move Penelope and Odysseus' wedding bed taking into account that Odysseus knows the secret about the bed. When Odysseus tells her that moving the bed is impossible because the frame was attached to an olive tree within the room, Penelope is finally convinced that he is Odysseus.