Question

The radius of the larger circle in the first quadrant and touching the line $4x+3y-12=0$ and the co-ordinate axes is

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is B $6$

Equation of circle touching coordinate axes in $1^{st}$ Quadrant is given by -
S: $(x-r{)}^2+(y-r{)}^2=r^2$
Circle S also touches the line $4x+3y-12=0$
Then the distance of $(r,r)$ from $4x+3y-12=0$ is $r$
$\therefore r=\left|\frac{4r+3r-12}{5}\right|$
$5r=|7r-12|$
$5r=7r-12$ or $5r=12-7r$
$r=6$ or $r=1$
Thus, the radius of larger circle is $r=6$.