The main fire pump for hydrants typically has a capacity to deliver a high volume of water, which is essential for effective firefighting. A standard capacity for these pumps is around 4500 litres per minute (lpm), which allows for sufficient water pressure and flow to fight fires in various buildings or structures.
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.