From the 1:60 rule;
On a 12nm arc, every 5 degrees is one mile. So assuming you have to fly 25 degrees of an arc before intercepting the inbound course, that would equate to 5 track miles. So you have 5nm on the arc + 12nm inbound = 17nm. So as you enter the arc you want to be around 17 x 300 = 5100ft AGL (approx.). Now you can project this point backwards to find your TOD.
For a 10nm arc just do the same thing with 6 degrees = 1nm.