Homeowners insurance may be helpful.
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Call your homeowner's insurance carrier. I doubt they'll cover the loss, but I don't think you have any other coverage available to you.
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Maybe your auto insurance
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As the other esteemed counsel have pointed out, you may look to your auto insurer or homeowners insurer to cover the claim. But at this point, it doesn't sound like the bicyclist has any real right to recover money from you. What would be his theory of why you are responsible for the fall? At this point, you may be best off to simply do nothing and hope that he goes away. If he does ultimately sue you, you will want to try to get one of your insurers to provide your defense. If they refuse to do so, consider retaining a lawyer on your own. See if you can negotiate flat fee representation.
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