Let the tangent to the circle  x2+y2=25at the point R3,4 meet x-axis and y-axis at points P and Q respectively. If r is the radius of the circle  passing through the origin O and having center at the incentre of the triangle OPQ, then r2 is equal to

The equation of the tangent to the circle x2+y2=25 to the circle at the point R3,4 is 3x+4y=25This line cuts the axes at two points ⇒P253,0,Q0,254The triangle OPQ formed. OP=253,OQ=254,PQ=12512The incentre of the triangle OPQ is I=2512,2512Hence the square of the radius is =OI2=252122=62572