1. Introduction: A poor farmer owns a magical goose that lays a golden egg daily.
2. Conflict: Driven by greed, he decides to kill the goose to get all the eggs at once.
3. Conclusion: The farmer finds no eggs inside, losing the magical goose and his fortune.
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. 