The line $3 x+4 y-24=0$ intersects the $x$-axis at $A$ and $y$-axis at $B$. Then the circumcentre of the triangle $O A B$ where $O$ is the origin is

• A

  $(2,3)$
• B

  $(3,3)$
• Correct answer
  C

  $(4,3)$
• D

  None of the above

Solution

Since circumcentre of right angled triangle lies on the midpoint of hypotenuse. So mid point of AB is $\left(\frac{0+8}{2}, \frac{6+0}{2}\right)$ or $(4,3)$

Hence, the correct answer is option: 'C'.