Say you want a semi-circle and you want to split it in half.
Here’s how you do it.
Draw your circle
Select the knife tool
Holding down the ‘Option’ key on your Mac, with your shape selected, drag the knife across the circle in a straight line.
Now you should be able to drag one shape away from the other. Except this doesn’t always work for me (sometimes the whole shape wants to move).
In that case bring up the ‘Path Finder’ Window and with your newly cut shape highlighted select the ‘Minus Front’ option. That should cut away the bottom half of your shape.
And Voila! Half a circle with a nice contour around all the edges.