Solve this following

If the line $3 x+4 y-24=0$ intersects the $x$-axis at the point $\mathrm{A}$ and the $\mathrm{y}$-axis at the point $\mathrm{B}$, then the incentre of the triangle $\mathrm{OAB}$, where $\mathrm{O}$ is the origin, is

  1. $(3,4)$

  2. $(2,2)$

  3. $(4,4)$

  4. $(4,3)$

Correct Option: , 2


$\left|\frac{3 r+4 r-24}{5}\right|=r$

$7 r-24=\pm 5 r$

$2 r=24$ or $12 r+24$

$r=14, \quad r=2$

then incentre is $(2,2)$


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