Charanka is located in Gujarat, India, and is known for its large-scale solar power production. The Charanka Solar Park is one of the largest in India and contributes significantly to the country’s renewable energy efforts.
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.