Circles Collection

Concentric Circles

 

The length of the red segment is 2. What is the area of the blue ring?

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Four Arcs and a Square

 

 

 

 

 

 

 

All arcs are congruent. What is the area contained by the four arcs as a fraction of the square's area?

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Ten Circles

The orange ring is 12 pi long. What is the total length of the blue rings? Their centers lie on the orange ring's diameter.

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Three Circles

The red point is the center of the larger circle. What is the ratio of the yellow area to the blue area?

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Circle, Square, Circle

 

 

 

 

 

 

 

The blue quadrilateral is a square. What is the ratio of the two circles' areas? 

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Circles vs. Squares

 

 

 

 

 

 

The two large circles have radii of 1. The dodecagon is made up of five squares. Which design contains the largest area: the four circles or the dodecagon?

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3 Circles or a Square?

 

 

 

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?

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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

 

 

 

 

 

 

 

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

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