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Finding random geographical point around given coordinates

In my current project, we are using Mongo 2dsphere index to sort records by distance from certain geographical point. It's very useful to sort large data sets by distance with good performance, but unfortunately it is not possible to use it if you need to extend your sorting rules (that is - sort by other fields as well).
What we needed was to randomize search results in a certain way, while retaining "sort by distance first" rule. Below is a function (in TypeScript), which proved to be very useful for this task. It returns a random geographical point anywhere around given coordinates with range limit in km. It was very interesting to find our that longitude and latitude are just sphere vector angles (https://en.wikipedia.org/wiki/Latitude), so a bit of trigonometry is expected.

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