Verified Solution • 2025–26 Session moderate

QJEEM24Ma1b57: JEE Main 2024 Mathematics - Class 11 JEEM24Ma1b57 Solution: Let ABCD and AEFG be squares of side 4 and 2 units,…

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 :

Multiple Choice Options

  • A r=1\mathrm{r}=1
  • B 2r2−4r+1=02 \mathrm{r}^2-4 \mathrm{r}+1=0
  • C 2r2−8r+7=02 \mathrm{r}^2-8 \mathrm{r}+7=0
  • D r2−8r+8=0\mathrm{r}^2-8 \mathrm{r}+8=0

Step-by-Step Verified Solution

JEE Main 2024 (Online) 5th April Evening Shift Mathematics - Circle Question 9 English Explanation

CF=42−22=22=r+r2C F=4 \sqrt{2}-2 \sqrt{2}=2 \sqrt{2}=r+r \sqrt{2}

amp;⇒(2−r)2=ramp;⇒2=(r2−r)⇒2=r2(2−r)2amp;⇒2(r2−4r+4)=r2amp;⇒r2−8r+8=0\begin{aligned}& \Rightarrow \quad(2-r) \sqrt{2}=r \\& \Rightarrow \quad \sqrt{2}=\left(\frac{r}{2-r}\right) \Rightarrow 2=\frac{r^2}{(2-r)^2} \\& \Rightarrow 2\left(r^2-4 r+4\right)=r^2 \\& \Rightarrow r^2-8 r+8=0\end{aligned}

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