JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let \(\mathrm{ABCD}\) and \(\mathrm{AEFG}\) be squares of side \(4\) and \(2\) units, respectively. The point \(\mathrm{E}\) is on the line segment \(\mathrm{AB}\) and the point \(\mathrm{F}\) is on the diagonal \(\mathrm{AC}\). Then the radius \(r\) of the circle passing through the point \(\mathrm{F}\) and touching the line segments \(\mathrm{BC}\) and \(\mathrm{CD}\) satisfies :
- A \(r=1\)
- B \(\mathrm{r}^2-8 \mathrm{r}+8=0\)
- C \(2 r^2-4 r+1=0\)
- D \(2 r^2-8 r+7=0\)
Answer & Solution
Correct Answer
(B) \(\mathrm{r}^2-8 \mathrm{r}+8=0\)
Step-by-step Solution
Detailed explanation
\( \mathrm{OF}^2=\mathrm{r}^2 \) \( (2-r)^2+(2-r)^2=\mathrm{r}^2 \) \( \mathrm{r}^2-8 \mathrm{r}+8=0\)
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