How does Bilbo get Smaug to reveal Smaug's weak spot?
In The Hobbit by J. R. R. Tolkien, Bilbo is a Hobbit on an adventure. At one point during the story, he must enter the lair of the dragon Smaug, underneath a mountain. When he enters, Smaug is sleeping. There is a huge pile of treasure in the dragon's lair. Bilbo, invisible because he is wearing the Ring, works up the courage to sneak out a single golden goblet. The dwarves outside are excited to see the treasure. However, when the dragon awakes, he can tell exactly what is missing. He flies outside and searches for the thief, sitting atop the mountain. Bilbo and the dwarves must hide inside the mountain. Smaug eventually returns inside and pretends to sleep. When Bilbo comes back in to attempt to find the dragon's weak spot, Smaug "awakes" and smells the intruder, who is once again invisible. Bilbo and the dragon engage in conversation, but Bilbo outwits the dragon with riddles and flattery, soon tricking Smaug into revealing his own weak spot. Specifically, he uses compliments to imply that he believes Smaug to be a great and indomitable dragon with not a single weakness. He convinces Smaug to show him the strength of the armor on his belly. Smaug is happy to show off, saying "My armour is like tenfold shields, my teeth are swords, my claws spears, the shock of my tail a thunderbolt, my wings a hurricane, and my breath death," and when he rolls over, Bilbo spies the telltale signs of the dragon's weak spot.
Bilbo flatters Smaug the dragon, tricking him into rolling over so he can see the weak spot on his belly.
In chapter 12, “Inside Information,” Bilbo tricks Smaug into showing his weak belly. Thorin reminds Bilbo that, “every worm has its weak spot” and Blibo tricks Smaug into showing his. Bilbo faltters Smaug, calling him “Smaug the Impenetrable” and praising his “waistcoat of diamonds.” Biblo had already noticed the “peculiar undercoating” and wanted a closer look. By describing him as impenetrable and praising his waistcoat, he lures Smaug into a false sense of security and plays on his pride. Bilbo thinks to himself,
“Old fool! Why there is a large patch in the hollow shell of his left breast as bare as a snail out of its shell!” (chapter 12)
Bilbo soon shares this information so the others can bring him down.