Answer: The radius is 13.
Draw OP ⊥ MN. The perpendicular from the centre bisects the chord, so MP = \(\frac{25}{2}\) = 12.5, and LP = MP − ML = 12.5 − 9 = 3.5.
In right-angled \(\triangle OPL\):
\[OP^2 = OL^2 - LP^2 = 25 - 12.25 = 12.75\]In right-angled \(\triangle OPM\):
\[OM^2 = OP^2 + MP^2 = 12.75 + 156.25 = 169\] \[OM = 13\]