A tragic hero is a protagonist that has a fatal (tragic) flaw; usually, the audience finds sympathy with the hero.
At the beginning of the play, Lear seems like a fine ruler and in his generosity, he decides to divide his kingdom equally among his daughters. But then he encourages his daughters to compete by pledging their love for him. When Cordelia refuses to make overly dramatic praises, as her sisters do, Lear's pride takes over and he essentially disowns her and then banishes her.
The barbarous Scythian,
Or he that makes his generation messes
To gorge his appetite, shall to my bosom
Be as well neighboured, pitied, and relieved
As thou, my sometime daughter. (I.i.114-18)
(The "barbarous Scythian" was a savage nomad and "makes his generation messes" refers to making a meal (eating) of parents or children. Here, Lear says that he will treat Cordelia as he...
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