Let $A B C D$ and $A E F G$ be squares of side 4 and 2 units, respectively. The point $E$ is on the line segment $\mathrm{AB}$ and the point $\mathrm{F}$ is on the diagonal $\mathrm{AC}$. Then the radius $\mathrm{r}$ of the circle passing through the point $\mathrm{F}$ and touching the line…

Question

Let $A B C D$ and $A E F G$ be squares of side 4 and 2 units, respectively. The point $E$ is on the line segment $\mathrm{AB}$ and the point $\mathrm{F}$ is on the diagonal $\mathrm{AC}$. Then the radius $\mathrm{r}$ of the circle passing through the point $\mathrm{F}$ and touching the line segments $\mathrm{BC}$ and $\mathrm{CD}$ satisfies:

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{OF}^2=\mathrm{r}^2 \ & (2-r)^2+(2-r)^2=\mathrm{r}^2 \ & \mathrm{r}^2-8 \mathrm{r}+8=0\end{aligned}$

Let $A B C D$ and $A E F G$ be squares of side 4 and 2 units, respectively. The point $E$ is on the line…

Solution