Category Archives: Circles in a Square

Solution to November 25, 2019′s Challenge

Posted on November 26, 2019 by kevin

By connecting various points in the figure, we have the following: It is obvious that the radius of each quarter circle is $\dfrac{\sqrt{2}}{2}$, and the area of two green regions is: $$\dfrac{1}{2}-\dfrac{1}{4}\cdot\pi\cdot(\dfrac{\sqrt{2}}{2})^2=\dfrac{1}{2}-\dfrac{\pi}{8}$$ Therefore, the total area of the blue regions … Continue reading →

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Problem of the Day – November 25, 2019

Posted on November 25, 2019 by kevin

In the following figures, 4 quarter circles join at the center of a unit square. Find the area of the shaded regions in blue.

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Problem of the Day – November 24, 2019

Posted on November 24, 2019 by kevin

In the following figure, a semi-circle is inscribed with maximum size inside a unit square. Find the radius of the the semi-circle. 

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Circles in a Square – Part 3

Posted on November 23, 2019 by kevin

By adding one more quarter circle, we have the following figure. The question is: what is the area of the region bounded by arc $\stackrel \frown {AE}$, $\stackrel \frown {EF}$ and $\stackrel \frown {FA}$? In fact, based on the calculations … Continue reading →

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Circles in a Square – Part 2

Posted on November 22, 2019 by kevin

Continuing this topic, look at the following diagram, with two quarter circles in a unit square, the question is: what are the area of of each of the 4 regions inside the square? To answer the question, we need to draw … Continue reading →

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