Category Archives: Circles in a Square

As shown in the figure, $ABCD$ is a square, $E$ is the mid-point of $AB$. The circle with its center at $H$ is tangent with $AD$, $AE$ and $DE$. The circle with its center at $F$ is tangent with $BC$, … Continue reading →

In this 10th post of this series, consider the following figure with two co-tangent semi-circles drawn, centered at point $E$ on $\overline{AB}$ and $F$ on $\overline{BC}$. A full circle centered at point G, tangent with both semi-circles, line $\overline{AD}$ and $\overline{CD}$ in a unit square $ABCD$. Find … Continue reading →

Continue the topic of the previous post in this series, if we construct a semi-circle first, then a quarter circle, and finally a full circle, as the following, what the radius of the full circle? The problem is harder than the … Continue reading →