JEE Math Practice Question

Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies :

1. A.$$\mathrm{r}=1$$
2. B.$$2 \mathrm{r}^2-4 \mathrm{r}+1=0$$
3. C.$$2 \mathrm{r}^2-8 \mathrm{r}+7=0$$
4. D.$$\mathrm{r}^2-8 \mathrm{r}+8=0$$