The line 2x - y + 1 = 0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x - 2y = 4. The radius of the circle is

2x - y + I = 0 is a tangent. Slope of line OA=−12 The equation of OA is(y−5)=−12(x−2)  or  x+2y=12  Therefore, intersection with x−2y=4 will give the coordinates of center as (8, 2). Hence, r=OA=(8−2)2+(2−5)2=35