AoPS Wiki talk:Problem of the Day/July 24, 2011
Solution to Problem 1: If the circumference is , then we can find the radius. Because of our cirumference formula, we know that . So, the radius is units. We can insert this into the circle area formula to find the area: . So, the area is .
Solution to Problem 2: Rearrange the terms on the left side:
This is just
This is trivial, so the inequality must be true. (Idea for wording of the end of the solution: solutions for the Pre-Olympiad Inequalities marathon by other users)