Let C 1 and C 2 be two circles of radius r 1 and r 2 units respectively touching both the axes. If the two circles are orthogonal, then r 1 r 2 + r 2 r 1 is equal to

Step-by-step solution

Let the equation of the circle be x - r 2 + y - r 2 = r 2 and x 2 + y 2 - 2 r x - 2 r y + r 2 = 0 If they are orthogonal 2 - r 1 - r 2 + 2 - r 1 - r 2 = r 1 2 + r 2 2 ⇒ r 1 2 - 4 r 1 r 2 + r 2 2 = 0 ⇒ r 1 r 2 + r 2 r 1 = 2 - 3 + 2 + 3 = 4