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Contact tracing requires a strong understanding of the context of a user, and location with other sensory data could provide a context for any infection encounter. Although Bluetooth technology gives a good insight into the proximity aspect of an encounter, it does not provide any location context related to it which helps to make better decisions. Using the ideas presented in this paper, one shall be able to obtain this valuable information that could address the problem of false-positive and false-negative to a certain extent. All of this within the purview of Google/Apple Exposure Notification (GAEN) specification, while preserving complete user privacy. There are four ways of propagating context between any two users. Two such methods allow private location logging, without revealing the location history within an app. The other two are encryption-based methods. The first encryption method is a variant of Apple's FindMy protocol, that allows nearby Apple devices to capture the GPS location of a lost Apple device. The second encryption is a minor modification of the existing GAEN protocol so that global context is available to a healthy phone only when it is exposed - this is a better option comparatively. It will still be the role of Public Health smartphone app to decide, on how to use the location-time context, to build a full-fledged contact tracing and public health solution. Lastly, we highlight the benefits and potential privacy issues with each of these context propagation methods proposed here.