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AoPS Wiki:Problem of the Day/July 24, 2011

Problem 1 (Easier): A circle has a circumference of $18\pi$. What is the area of the circle?

Problem 2 (Harder): (Idea/inspiration: Art of Problem Solving's Intermediate Algebra/AoPS Wiki page content posted by another user) Where $a, b, c \in \mathbb{R}$, why must the following be true?

$a^2 + c^2 + 2ab + 2ac + b^2 + 2bc \geq 0$

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