The law does not give a strict answer to this kind of question. What happens in law is that the law provides conduct duties and a jury decides in a given case whether a duty was not met. The duty that applies to injury cases is that the people involved must use that same level of being careful that a reasonable person would have used under similar circumstances. If someone fails to do that and someone else gets hurt as a result of that failure, then the injured person can recover for the injuries.
As long as you acted like any other reasonable person would have acted, then you are not liable. So I cannot give you an exact answer, except to say that, if it was just a mistake on the part of the bicyclist in misinterpreting your wave, then maybe no one was legally "at fault."
You should notify your insurance company, and let them handle things, though. And don't worry, they won't pay if it was not your fault (they try not to pay even if it was).
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
First, report the incident to your insurance carrier. From the facts, I would argue that you were not at fault, however, others may disagree. If you vehicle was not moving at the time, that helps your case.
It's called a "wave on case" in which a person who waves may be liable. Simply report the matter to your insurance company to resolve.
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