Chubukov thinks Lomov is a perfect match for his daughter, Natalya, and has been waiting for this marriage proposal. When Lomov worries about whether Natalya will accept, Chubukov assures him that she is in love with him. Despite this, throughout the play, Natalya argues with Lomov about everything. After one such argument, when Lomov leaves, Chubukov tells Natalya that Lomov has come to propose to her. Upon hearing this, Natalya starts crying and begs her father to bring Lomov back immediately. Her words, "Ah! Bring him back! Back Ah! Bring him here. Quick, quick! Fetch him!" show that she really does love him.
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 $\sin 2\theta$. 