Bilbo had seen it during his conversation with Smaug and later a bird heard Bilbo talk about the missing bit of armor. The bird told Bard where Smaug's vulnerable spot was; one spot under his arm where there was no armor.
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The old thrush flew down and told him, and Bard found he could understand the bird's language.
He used his mighty black arrow and shot Smaug in the hole in his armor on his breast.
The thrush, who had overheard Bilbo Baggins telling of Smaug's unprotected patch.
He inherited it from his father. Who had gotten it from his father. It was originally from one of the great elven cities.
He had a black arrow, forged many years before that may have had magical properties. And a thrush told him about the bare patch under his arm that Bilbo had spotted earlier.
Bard the Bowman shot a black arrow into the bare hollow in Smaug's left breast, killing the dragon. The arrow was believed by Bard to have come from the King Under the Mountian, and his father and his grandfather had used it.
The Old Thrush, one of the species of Great Thrush that lived in the Esgaroth region, told Bard that Smaug had a hole in his armored chest right over his heart.
The killer of Smaug is Bard the Bowman. He's alerted by a thrush who overheard of Smaug's weakness (a single bare spot in his bejeweled chest).Bard, a man in the town of Esgaroth, a town by the lake, killed the dragon. He was told by the thrush where Smaug's weak spot was, and thus Bard was able to shoot the dragon through the heart.
Bard shoots Smaug with his black arrow.
The thrush who overheard Bilbo tell the dwarves about the "soft spot" in Smaug's armor relayed this information to Bard the Bowman. (For some reason people from Bard's lineage were able to understand the language of thrushes.) Bard, using the thrush's advice, shot his black arrow into the hollow of Smaug's chest, thus killing him.