In \(\Delta DAC, \stackrel\frown{DAC} = \theta\) \(\sin \theta = \frac{5}{13}\) \(\theta = 22.6^\circ\) \(< DOC = 22.6^\circ \times 2 = 45.2^\circ\) \(\sin 45.2 = \frac{5}{r} \implies r = \frac{5}{\sin 45.2}\) \(r = 7.046cm\) = \(7\frac{1}{24} cm\)