The Sashastra Seema Bal (SSB) is the paramilitary force responsible for guarding the Indo-Nepal Border. The force is also tasked with maintaining border security, preventing illegal activities, and assisting with disaster relief.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.