Category Archives: Circles in a Square

Continue the same topic of the previous post in this series, a line is drawn between point L and the tangent point M between the full circle and the quarter circle, as shown in the following figure. Prove $\triangle{HLM}$ is a right triangle. Based on … Continue reading →

Continue the topic in the previous post of this series, we add another circle inscribed in the area bounded by one side of the unit squares, the simi-circle and the quarter-circle, as the following. What is the radius of the … Continue reading →

Look at the following figure, a simi-circle is inscribed between the quarter circle and one side of the unit square. What the radius of the semi-circle? Obviously, $G$ is the center of the semi-circle, line $\overline{CG}$ crosses $F$, the tangent … Continue reading →

Today, we talk about a classic problem of packing circles in a square. Given a unit square, you need to make 3 congruent, non-overlapping circles that are as big as possible. It has been proven that the arrangement of 3 circles must be as the following. Can … Continue reading →

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 →