Basic Layout Question

Thanks everyone for your responses. You can't tell in the photo but the part is actually about 3/4" thick. The seting up on a vee block and scribing at half the diameter sounds like the most accurate (as far as layout). But for quick (two deciamal :) ) work I'm liking the two arc methode.
 
A little complex, but if accuracy was important I would make a stub the inside diameter and center it on the lathe. Once there was a center point, arcs could be drawn to provide an accurate 90* crossing. Basic grammar school geometry. . .

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Basic geometry and old school drafting tricks.

First since it is solid and not on paper we need to add a step.

If on paper the point I need is where line crosses arc or circle, you do not really have a flat spot there so set the blade on your center finder so when placed on either side in same orientation you have the end of the rule about 1/4 inch from the outside edge.

Next use either a divider compas or the points of your caliper to strike some arcs.

You will place one point on the cross point you just made.

Adjust the other point so it is just past 1/2 way across and can strike an arc near the center of the disk towards the outside.

Do this 4 ties, 2 from each end and to both sides.

Where these arcs cross will be dead center between the 2 cross marks and 90 degrees to your vertical.

Reset your center marker to full length and align the edge on the points where arcs cross and scribe your line.

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Since the part has thickness, here is how I would do it.

I would mount the part on my mill table and use my edge finder to find the edges in the x direction. My DRO has a center feature which will zero it a half the difference between the left and right edges. If care is taken to use the same y position for finding each edge and the y zero is reasonably close to the center, a single pass is sufficient. Next, with the spindle set at the x zero position repeat for the y direction. If the x center is suspect, the centering process for the x axis can be repeated. The spindle should now be centered on the part to better than .001". (I can get this to+/-.0001").

If scribed lines are the final objective, a scribe can be mounted in the spindle and dragged across the part to scribe the lines. The accuracy will be as good as your scribe runout allows. To provide minimal runout, dress the scribe after mounting it in the spindle. Perpendicularity of the lines will be as good as your mill. If machining is the final objective, forget about scribing and just go directly to the machining.

While I would use the DRO on my mill, it can be done by the dials with a little more effort. 1st, you will need to account for backlash and 2nd, you need to do some basic arithmetic.
 
I would clamp it to an angle plate with one edge flush wth the edge of the plate. Use a surface gauge or height gauge with scriber. Set the scribe point to 1/2 diameter above the surface plate. Scribe one line then flip the angle plate on its side and scribe the other line.
 
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