Highlight image region based upon segment of fitted circle within imagej

Highlight image region based upon segment of fitted circle within imagej

I need to conduct some manual counting and sizing analysis on some
particles within a set region of a circle using imagej. I think this
problem can be best explained with the schematic below:

All the images contain just over half a circle and this is the main region
of interest (the blue circle in the image). I would like to count/size the
contents of one third of it (the region highlighted in gray). Here is what
I would like an automatic macro to do when I open an image of interest:
1) Using something like ThreePointCircularROI fit a circle and find its
centre 2) Draw two lines +60 degrees and -60 degrees from the vertical
extending from the centre of the circle to the edge of the image (the red
lines in the image).
My intention is then to count all particles within the gray region
manually since my images are complex. Setting this bounding area will mean
I always count the same area in each photo.
Thanks for any help.