In book 19, who discovers Odysseus identity? Explain and cite a quote to support your answer

While Eurykleia bathes him, she recognizes an old hunting wound on Odysseus' thigh and exclaims that the beggar is Odysseus,

"Odysseus sat by the fire, but ere long he turned away from the light, for it occurred to him that when the old woman had hold of his leg she would recognize a certain scar which it bore, whereon the whole truth would come out."