Bholi's teacher played an important role in changing the course of her life. She was polite and friendly which touched her heart. She encouraged her every time and was affectionate towards her. The teacher transformed her into a confident person who could read, write and speak clearly.This gave her the required confidence. Moreover, teacher’s appreciation and encouragement helped her overcome her low morale.
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 $\sin 2\theta$. 