Stains can often be identified by their color and smell. For example, food stains like ketchup or curry have distinct colors and smells that can help determine their source. The combination of color and odor is often a key indicator in identifying stains.
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.