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

Line intersects the x-axis at x=8, y=0 ⇒ A=(8,0)
Line intersects the y-axis at x=0, y=6 ⇒ B=(0,6)
Incenter of triangle OAB = (ax1+bx2+cx3)/(a+b+c), (ay1+by2+cy3)/(a+b+c)
Where O=(x1,y1)=(0,0), A=(x2,y2)=(8,0), B=(x3,y3)=(0,6)
⇒ AB=10, OB=6, OA=8
⇒ Incenter = (10.0+6.8+8.0)/(10+8+6), (10.0+6.0+8.6)/(10+8+6)
⇒ incenter = (2,2)