That really does resemble a bull's eye rash to me. I have looked at many pictures of bull's eye rashes and they are all a little different.
Mine had a red circle in the middle along with the red circle outside, but the red in the middle was where I got bit.
Some have been bitten and the rash does appear in a totally different spot so the red center bite mark is not there. But a circular rash is lyme.
Here are your pictures:
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