I do that using MS Publisher but I would think most DTP programs would be able to do the job.
Drawing your circle is as you say easy. Mark the centre point with a verticle and horizontal line. select all and combine into a single image .Now use a bit of triganomitry and draw a triangle having sides of 3,4 and 5 units in length. Move these around until they link up into a triangle. You will have produced a triangle whose angles are 30,60,and 90 degrees. Select all and link them together so that they can be moved about as a complete triangle. Place the point of the 30degree corner on the centre point and you will have established either a line to mark the position of the 2 oclock and 8 oclock points. Copy and paste the triangle and using the copy to move around and fix the 1 oclock and 7 oclock poimts.
If you have followed so far you shold have no trouble completing the face.
Remember when you are satisfied with each stage to select all and combine everything together as you go to avoid losing your work by making the wrong movement.
I hope this helps but post back if you need more