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

Step-by-step solution

2 x - y + 1 = 0 is tangent to the circle Slope of line O A = - 1 2 Equation of O A ,   y - 5 = - 1 2 x - 2 2 y - 10 = - x + 2 x + 2 y = 12 ∴ intersection with x - 2 y = 4 will give coordinates of centre On solving, we get, the centre of the circle is ( 8,2 ) The radius OA = 8 - 2 2 + 2 - 5 2 = 36 + 9 = 45 = 3 5 units Hence, O A 2 = 45