A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. The distances from the end points A, B of the side AB to the tangent at O are equal to m and n respectively. Then, the diameter of the circle, is

Let the coordinates of A and B be (a, 0) and (0, b) respectively. Since the triangle OAB is a right angled triangle, the centre of the circumcircle is the mid point of AB i.e. (a/2,b/2) and the radius is equal to 12AB=12a2+b2The equation of the circumcircle is x2+y2−ax−by=0The equation of the tangent at the origin to this circle is ax+by=0.∴ m=a2a2+b2 and n=b2a2+b2⇒ m+n=a2+b2= Diameter of the circle.