SSC CPO 2023 PYQ — Question 113

The correct answer is Option 4 i.e. $\sqrt 108+\sqrt 189$.

Given AB = 12 cm

We know that the line joining both centers cut the common chord into two equal parts then,

AC = 12/2 = 6 cm

Now, applying Pythagoras theorem in triangle O₁AC

⇒ O₁A² = O₁C² + AC²

⇒ O₁C² = O₁A² - AC²

⇒ O₁C² = 15² - 6²

⇒ O₁C² = 225 - 36

⇒ O₁C = √189

Similarly, In triangle O₂CA

⇒ O₂A² = O₂C² + AC²

⇒ O₂C² = O₂A² - AC²

⇒ O₂C² = 12² - 6²

⇒ O₁C² = 144 - 36

⇒ O₁C = √108

The distance between their centres = √189 + √108