How to represent approximate points on a map?

Let's say we can display exact and approximate points on a map. Approximate points have a constant distance from an exact point. Which means they lie on the circle described by this distance, where the distance is the radius of the circle.

Exact points can be displayed as dots, circles, or pointers. But how should I display approximate points? I have the following initial thoughts:

  1. Show as a circle, in a different color than an exact point. The circle can be made more transparent with each zoom-in. There are a few ideas for showing list of locations when we are close enough, when circle is full sized on a screen, or when it's similarly as a dot as exact points.
  2. Show as a dot similar to that used for exact points but in a different color. A legend with be provided for the user to differentiate between the two dots.

There are some extremely important points to consider:

  1. map can be zoomed in and out
  2. points could be close, so their area of approximation could intersect
  3. It would be better if approximate points are a little bit less visible / remarkable
  4. possible to display area polygons
  5. exact and approximate points should be clickable. But there is also the option of making approximate points clickable from UI elements external to the map, for example a list.

Could you suggest any other approaches?