If one of the diameters of the circle x 2 + y 2 - 10 x + 4 y + 13 = 0 is a chord of another circle C , whose center is the point of intersection of the lines 2 x + 3 y = 12 and 3 x - 2 y = 5 , then the radius of the circle C is

Step-by-step solution

Given, S 1 ≡ x 2 + y 2 - 10 x + 4 y + 13 = 0 with radius R = 4 and its one diameter is chord of other circle S 2 whose centre is given by intersection of 2 x + 3 y = 12 & 3 x - 2 y = 5 which is 3 , 2 Now, plotting the diagram we get, Now, from above circle the distance between the centres is given by l = 5 - 3 2 + - 2 - 2 2 = 20 Hence, radius of S 2 will be, r 2 = 20 2 + 4 2 = 20 + 16 = 36 ⇒ r = 6