The Armed Forces (Special Powers) Act (AFSPA) of 1958 is a law that grants special powers to the Indian Armed Forces in areas declared as ”disturbed” under this law. One of the states where this Act is implemented is Manipur, especially in conflict zones. AFSPA is also in force in other parts of India such as Jammu and Kashmir and Nagaland.
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.