Maximize It! Collection

3 Circles or a Square?

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The brown circles are congruent. The one on the left contains three identical circles, the one on the right  inscribes a square. Which design maximizes the yellow area?

Two Intersecting Circle

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Where should the two moving points be placed for the pink segment to be at its maximum possible length?

Area of a Quadrilateral

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Determine the position of the orange chord such that the area of the blue quadrilateral is maximum.

Rotating Square

square rotating around the center of another square

The dot represents the center of the square. Find the position of the blue square such that the overlapping area (as a fraction of the orange square's area) is maximum.