circle

BD² = (13 – 8) x (16 + 5) = 5 x 21 = 105

Since BD = DC, therefore by theorem of similar triangles AC = 2 OD = 2 x 8 = 16

Now, DC² + AC² = AD²

Or, BD² + AC² = AD²

Or, 105 + 16² = AD²

Or, AD =  √361 = 19 cm