Denote the corner of the room (0,0), the point of
contacts (0,r) and (r,0) and the point on the edge
in question (10,5).
Draw a triangle with these points (10,5), (r,5), and (r,r).
This is a right triangle with sides of length r-10, r-5, and
r. The pythagorean formula tells us that (r-10)2 +
(r-5)2 = r2. Solving for r yields
r=5 and 25.
Thanks to Nick Hobson for this one.
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