The equations are:
$x=r(t-\sin{t})$
$y=r(1-\cos{t})$
Lets say that $(x,y)=(1,2)$ for a point. How can I find the radius of the cycloid? I can't solve the mathematics equation: $$\frac{1}{t-\sin{t}}=\frac{2}{1-\cos{t}}$$
It's complicate for me to solve it. If I'll find it I would find $r$.
thanks
HINT: you have the equation $$1-\cos(t)=2t-2\sin(t)$$ then $t=0$ is one solution the other solution can be obtained by a numerical method, $$t\approx 1.401379455902473454923964650592$$