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Circle $G$ is inscribed in an equilateral triangle of side 2 .

(a) Prove that for every point $P$ on $G, P A^2+P B^2+P C^2=5$.

(b) Prove that for every $P$ on $G$ the segments $P A, P B, P C$ are the sides of a triangle whose area is $\frac{\sqrt{3}}{4}$.
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