Tell Me The Radius First!
An equilateral triangle is inscribed in a circle. Which of the following has a larger area?
The region inside the triangle, or the region outside the triangle but inside the circle?
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2 solutions
Moderator note:
Explanation of diagram:
Consider a regular hexagon inscribed in the circle. The alternating vertices form an equilateral triangle. From the dissection, it is clear that the equilateral triangle is equal in area to the region of the regular hexagon that excludes the triangle.
Thus, the region outside the triangle (which includes the region of the regular hexagon outside the triangle) is larger than the region inside the triangle.
