If the chord of contact of tangents from a point on the circle x 2 + y 2 = r 1 2 to the circle x 2 + y 2 = r 2 2 touches the circle x 2 + y 2 = r 3 2 , then r 1 , r 2 , r 3 are in:

Step-by-step solution

Let C 1   :   x 2 + y 2 = r 1 2 C 2 :   x 2 + y 2 = r 2 2 C 3   :   x 2 + y 2 = r 3 2 Let A B be the chord of contact of tangents from a point P x 1 , y 1 on the circle C 1 to the circle C 2 . So the equation of A B T = 0 ⇒ x x 1 + y y 1 - r 2 2 = 0 Since line A B touches the circle C 3 . By condition of tangency, The distance of the line A B from the centre of the circle C 3 = r 3 ,   | 0 . x 1 + 0 . y 1 - r 2 2 | x 1 2 + y 1 2 = r 3 As P x 1 , y 1 lies on C 1 , x 1 2 + y 1 2 =