Author Archives: kevin

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 →

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 →