Taekwondo is a martial art that originated in South Korea and is considered the national sport of the country. It is recognized globally for its unique emphasis on high, fast kicks and has become an Olympic sport.
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.