Category Archives: Circles in a Square

Circles in a Square – Part 4

Posted on November 30, 2019 by kevin

In the previous post of this series, we asked if the area of the region can be solved without using previous calculation. Look at the figure below, after drawing several lines by connecting several points: The fan area of $[AEF]$ is $\dfrac{\pi}{12}$, because line $\overline{AE}$ and … Continue reading →

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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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