Human skin is made up of four main layers: the epidermis, dermis, subcutaneous tissue, and the deeper layers of connective tissue. These layers protect the body and regulate temperature.
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. 