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Mathematics / Theorems
DifficultyHard

This problem asks whether a given set of points is convex or not. A set of points is convex if, for any two points in the set, the line segment connecting them lies entirely within the set.

About this solution: The candidate's solution is correct and demonstrates a level of completeness. The approach is straightforward and easy to understand.

Mathematics / Theorems
DifficultyHard

This theorem states that a triangle is isosceles if and only if the sum of the squares of its two shorter sides is equal to the square of its longest side.

About this solution: This solution is correct.

Mathematics / Theorems
DifficultyHard

The sum of the interior angles of a polygon with n sides is (n-2)*180 degrees.

About this solution: The candidate's solution is correct and demonstrates a good understanding of the problem. The approach is clear and concise.