Not Really Big Power

Algebra Level 3

Given that \[ 1= \frac {a}{b+c} + \frac {b}{a+c} + \frac {c}{a+b}, \]

what is the value of

\[ \frac {a^2}{b+c} + \frac {b^2}{a+c} + \frac {c^2}{a+b} ?\]

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