simply define a polar grid with the correct radius and off you go. parts will snap to the grid.
if you don;t have the updated altium with poar grids : here is an easy way to do it
on a mechanical layer : draw a little cross ( 10 mil by 10 mil. ) then draw an arc with the wanted radius using the cross as the centerpoint.
place 1 led
copy the little cross and place it centered on one of the pads of the led.
X-A
S-I and select the cross on the led pad
O-P and change rotation angle to whatever you need
E-C - click on the cross in the center of the circle
DO NOT MOVE THE MOUSE
E-P hit space bar to take one rotation step and hit enter
E-P-SPACe-ENTER
E-P-SPAVE-ENTER
and so on as many times as needed.
now delete the circle.
place led's the led's pin 1 will 'snap' to where the little crosses are. when moving the led hitting the spacebar will rotate the part with the right rotation as well
to define the inner large circle : place a circle on the keepout layer. put in th emech comments to use keepout as board contour.