If the line 3 x+4 y-24=0 intersects X and Y axes in points A and B respectively then incenter of the triangle O A B where O is origin is

Step-by-step solution

Incenter of triangle OAB with vertices at intercepts of line 3x+4y-24=0 The line 3x+4y-24=0 intersects the axes at A(8,0) (x-intercept) and B(0,6) (y-intercept), with O=(0,0) . Triangle OAB is right-angled at O with side lengths: OA=8 , OB=6 , and hypotenuse AB=10 . Using the incenter coordinate formula with a=10 opposite O , b=6 opposite A , and c=8 opposite B : x = 10 0 + 6 8 + 8 0 10+6+8 = 48 24 = 2 y = 10 0 + 6 0 + 8 6 10+6+8 = 48 24 = 2 Alternatively, for a right triangle with legs 8 and 6 , the inradius is r