In the story “His First Flight” by Liam O’Flaherty, the young seagull was afraid of flying despite it being a natural act for birds. His fear can be justified as follows:
The story teaches us that fear of the unknown can seem overwhelming, but taking the first step often leads to success.
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. 
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$. 