Solution:
Let the radius of the table be r. Point A is the center of the table. Triangle ABC is a right triangle. Therefore the Pythagorean Theorem can be used to solve for r:
(r 5)2 + (r 10)2 = r2
r2 10r + 25 + r2 20r + 100 = r2 which simplifies to
r2 30r + 125 = 0
This factors to (r 5)(r 25) = 0 (you can also use the Quadratic Formula)
The solutions are r = 5 and 25.
The case of
r = 5 is an interesting one (or a trivial one, depending on
your mood). This means the square room is just large enough to fit
the table, as shown in the picture on the left. Point P is 5
inches from one wall and 10 inches from the other, see?
A strange coincidence: no matter what size the table is, if there is a point that is twice as far away from one wall as the other, the table will have a radius thats five times the distance to the closer wall (in this case 25 = 5 x 5). I wonder why