I used Pythagoras to get an answer of 12.7 ft
On the diagram, the blue bar is the maximum distance that you can fit around the corner. We can construct a triangle (green) which, from the information given in the question is isosceles with the two sides of 9m.
To find the length of the blue line, which is the hypotenuse, use Pythagoras.
EDIT: Use Earboth's answer, it is better than mine