DVR (Digital Video Recorder) is an essential component of a CCTV system. It records and stores video footage captured by the cameras, allowing for later review and monitoring. Heat detectors and motion detectors are peripheral sensors, while the alarm is an alert mechanism.
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.