The radius of a circle whose center lies in the fourth quadrant and touches each of the three lines x=0, y=0 and 3 x+4 y-12=0 , is.... units.

Step-by-step solution

Given lines, aligned & l₁: x=0 & l₂: y=0 aligned l₃: 3 x+4 y-12=0 y= -3 4 x+3 Circle touches X -axis and Y -axis. Then, perpendicular distance from X -axis and Y -axis to center is same and let's say it r . Center =(r, r) Let circle touches l₃ at P . O P=r | 3 r+4 r-12 3^2+4^2 |=r r= 7 r-12 5 When r= 7 r-12 5 aligned & & 2 r & =12 & & r & =6 aligned and when -r= 7 r-12 5 12 r=12r=1