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} = r^{2}. Solving for r yields
r=5 and 25.

Thanks to **Nick Hobson** for this one.

Michael Shackleford, A.S.A.