Calculate circle position and size I have a question i can't solve and hope someone could help me
i have a canvas with lines on it. the lines contains 3 points total and i know each point coordinates (x, y)
The middle point angle of each of those line is always between 90-179
My problem is that i need to smooth the lines but i need the points of the curve that will be created to smooth the lines (1 point for each degree)
In my poorly made drawing you can see the lines and the red curve i need to create and know each of the curve points
the circle is just to show the curve creation process.. i don't need to create it but to know its center point and the points on my lines from which to start my arc
Hope i made it clear enough.. basically i need to make a good looking lines, it doesn't have to be super accurate or something 

 A: Call the three points $A$, $B$, $C$. The middle one is $B$, and that's the one we want to "round off". Let $U$ be a unit vector in the direction $A-B$, let $V$ be a unit vector in the direction $C-B$, and let $N$ be a unit vector in the direction of the bisector $U+V$. Suppose we want to round the corner with a radius $r$. In other words, we want to construct a circular arc of radius $r$ that is tangential to the lines $AB$ and $BC$.
Suppose the angle between $U$ and $V$ is $2\theta$. This means that the angle between $U$ and $N$ will be $\theta$.
The center of the desired circular arc is at the point $P = B + (r/\sin\theta)N$.
The circular arc touches the line $AB$ at the point $Q = B + (r\cot\theta)U$, and it touches the line $BC$ at the point $R = B + (r\cot\theta)V$. 
That gives you enough information to construct the arc. Here's a picture:

In CAD, the operation you're doing (smoothing out a corner with a circular arc) is called "filleting" or "rounding".
If you are a graphics programmer, it might be easier to do the rounding with Bezier curves, rather than circles.
