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ABC circle sector turns on ground (x axis) as shown in the figure. A is the center of the circle. $\angle{OAB}=\angle{OAC}=\alpha $

$|AB|=r$

$\cfrac{|AP|}{|PC|}=k$

The corners meet on point $H$ in the limit points. What is the curve equation $f(x)$ that passing from $P',P,P''$ Thanks for answers

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    @Berci Thanks for the link.It is si$m$iliar to Cycloid but turning point in circle in $m$y questio$n$, not on circle.2012-10-03

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This is a curtate cycloid. Refer to http://mathworld.wolfram.com/CurtateCycloid.html