Two common stitches in Kashida work are Satin and Chain stitches. Satin stitch is used for filling areas, while Chain stitch is used for outlining shapes.
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. 