I got the coordinates of the center of a circle $(a,b)$ as well as one other point $(x, y)$. From those I can derive the radius by applying square root to the result of following formula.
$$ (x-a)^2 + (y-b)^2 = r^2 $$
This should allow me to compute the angle but I have only this formula:
$$ x = a + r\cos t$$ $$ y = b + r\sin t$$
How can I compute $t$?
I am a bit lost in solving this system of equations. Any help?
You know $x, y, a, b$ and $r$. Then $$ \cos(t) = \frac{x-a}{r} = c_{1} \quad \text{and} \quad \sin(t) = \frac{y-b}{r} = c_{2} $$ Note that $c_{1}$ and $c_{2}$ are just two numbers that you compute based on what you know. How many solutions does each of the above trigonometric equations have in $t \in [0, 2\pi)$?
Of course, in the end, the right $t$ should satisfy both equations..