According to the Private Security Agencies Regulation (PSAR) of 2005, the training requirement for security guards includes a minimum of 90 hours of classroom instruction. This is designed to equip security personnel with essential skills related to law, security protocols, and emergency response.
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.