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 AB and the point F is on the diagonal AC . Then the radius r of the circle passing through the point F and

Correct answer: D. r^2-8 r+8=0 aligned & OF^2=r^2 & (2-r)^2+(2-r)^2=r^2 & r^2-8 r+8=0 aligned

JEE Main 20245 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 5 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Circle

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Circle

Let A B C D and A E F G be squares of side 4 and 2 units,...

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: 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 AB and the

Options

A $r=0$
B $2 r^2-4 r+1=0$
C $2 r^2-8 r+7=0$
D $r^2-8 r+8=0$

Correct answer

D. $r^2-8 r+8=0$

Step-by-step solution

\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}

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