HTML Canvas draw arc between two points

Question

I have found similar questions out there, but no answer. I have sketched a circle like so

ctx.strokeStyle='rgb(0,0,0)';
ctx.lineWidth=10;
ctx.beginPath();
ctx.arc(100,100,45,0,Math.PI*2,true);
ctx.closePath();
ctx.stroke();

which gives a circle situated at (100,100) with radius 45, plus 5 for the linewidth, making it a circle of radius 50. Now, I want to sketch the exact same circle, but another color, and only 1/4 of the original circumfrance (think the XBOX 360 red ring of doom). So I tried this

ctx.strokeStyle='rgb(0,250,0)';
ctx.lineWidth=10;
ctx.beginPath();
ctx.arc(100,100,45,0,Math.PI/2,true);    //use 1/4 of original angle
ctx.closePath();
ctx.stroke();

But that has the really annoying aspect of connecting the first and last points (sometimes I wonder who created the canvas element, like when embedding text, but don't get me started on that...)