First of all, nice viz!
I like the shapes you use.
I don't think there's a ready for use function for your requirement.
But one workaround I can think of is,
1) use a parameter to select a point instead of click.
2) write a long long calculated field (logical) to find the points with the distance (eg 10ish mile), using latitude/longitude, see Finding distances based on Latitude and Longitude
3) use the calculated as highlighter
The you can get something like this.
This is a very simple demostration and is attached for your reference.
distance.twbx 14.0 KB
I know this isn't exactly what you're after, but you can do a manual radial select. Click on the map and press S (or select Radial from the map options), then click and drag and you get a circle with the radius shown in miles.
Maybe that would help ?