Practice problem
Perpendicular Bisectors
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A rare Pokémon has appeared on your radar, you think it might be a Lapras, and you're trying to track it down. As you're walking down a straight road, you notice that our radar changes its distance indicator from 3 footprints (within 1km) to 2 footprints (within 100m) at point A. Then, after walking another 100m, the distance indicator goes back up to 3 footprints at point B.
It turns out there are now only two precise spots it can be! Both possible spots are a certain distance away from the point halfway between A and B, along a direction perpendicular to your road. What is that exact distance in meters, rounded to the nearest whole number?