Consider circles C 1 and C 2 touching both the axes and passing through 4 , 4 , then the x -intercept of the common chord of the circles is

Step-by-step solution

Since the circle touches both the axes and passes through 4 , 4 , it lies in the first quadrant, so its equation is x - r 2 + y - r 2 = r 2 4 , 4 lies on it, hence r 2 - 16 r + 32 ⇒ r 1 + r 2 = 16 C 1 is x - r 1 2 + y - r 1 2 = r 1 2 C 2 is x - r 2 2 + y - r 2 2 = r 2 2 Equation of the common chord is 2 x - r 1 + r 2 + 2 y - r 1 + r 2 + r 1 + r 2 = 0 ⇒ x + y = 8 Hence, the x -intercept is 8