Draft:Bpow50

The following problem was suggested by Al Zimmermann. Many Thanks!

A mathematics professor and four mathematics students are in a square room, 10 feet on a side. The four students are stationed at the room's four corners, each student armed with a water pistol having a range of 10 feet. What is the area of that portion of the room in which the professor is simultaneously in range of all four water pistols?

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.