Normal to Cycloid passes through Bottom of Generating Circle

Theorem
Let $C$ be a cycloid generated by the equations:
 * $x = a \left({\theta - \sin \theta}\right)$
 * $y = a \left({1 - \cos \theta}\right)$

Then the normal to $C$ at a point $P$ on $C$ passes through the bottom of the generating circle of $C$.