Refer to the figure below with the labeled points:
Your error was that you thought x stood for AB when
it really only stood for AD, and so you found the
entire hypotenuse correctly as 13. But that was AB.
To get AD you must subtract BD. Now both BC and BD
are radii of the same circle, and since all radii of
a circle are equal in length, and BC = 5, then BD is
also 5 and to find x you must subtract BD, which is 5,
from AB, which you calculated as 13, and get x = 8.
Edwin
