Consider the +X axis and the +Y axis to be the corner. The table has radius r which puts the center of the circle at (r,r) and makes the circle tangent to both axis. The equation of the circle (table's perimeter) is
(x-r)^2 + (y-r)^2 = r^2 .
This leads to
r^2 - 2r(x+y) + x^2 + y^2 = 0
Using x = 10, y = 5 we get the solutions 25 and 5. The former is the radius of the table. Its diameter is 50 cm.
The latter number is the radius of a table that has a point which satisfies the conditions but is not on the quarter circle nearest the corner.