The ”Buttonhole stitch” is a variation of the chain stitch. It is commonly used in embroidery for finishing edges or creating decorative borders. In this stitch, the needle is inserted in a looped manner similar to chain stitch, but it is more structured and often used to create a raised or outlined effect, making it more rigid compared to the chain stitch.
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. 