How does DeepSeek-R1 "think"?
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QUESTION: I f the center of a hexagon is located at a (0,0) coordinate, which are the coordinates of each vertex if the length of the side of the hexagon is 10 mm? Analyzing and reasoning phase Okay, so the user wants to find the coordinates of each vertex of a hexagon centered at (0,0) with a side length of 10 mm. Let me think about how to approach this. First, I remember that a regular hexagon can be inscribed in a circle. Each vertex is equally spaced around the circumference. The key here is relating the side length to the radius of the circumscribed circle. Wait, is the radius the same as the side length? Hmm, no, I think that's only true for a hexagon with a side length equal to the radius. Wait, actually, in a regular hexagon, the side length is equal to the radius of the circumscribed circle. Let me confirm that. In a regular hexagon, all sides are equal, and all internal angles are 120 degrees. The radius of the circumscribed circle (distance from center to a vertex) is ...