CBSE Class 10 Maths (Standard) 2016 · Paper 30/3 · Question 24

In Fig. 8, two equal circles, with centres $O$ and $O^{\prime }$, touch each other at $X$. $O{O}^{\prime }$ produced meets the circle with centre $O^{\prime }$ at $A$. $AC$ is tangent to the circle with centre $O$, at the point $C$. $O^{\prime }D$ is perpendicular to $AC$. Find the value of $\frac{D{O}^{\prime }}{CO}$.