A binary digit, or bit, is the most basic unit of information in computing. It can have only one of two possible values: 0 or 1. These values represent the two states of a binary system, which are used for processing and storing data in computers.
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.