Find angle NMK.

Triangle OMN is a right-angled triangle with ON=9 and OM=18. Since ON is the radius and MN is tangent at N, angle ONM is 90 degrees. In triangle OMN, sin(angle MON) = ON/OM = 9/18 = 1/2. Therefore, angle MON = 30 degrees. Angle OMN = 90 - 30 = 60 degrees. Since OK is perpendicular to NK, angle ONK = 90 degrees. Angle KNM = 90 degrees. Angle NMK = Angle KNM - Angle OMN = 90 - 60 = 30 degrees.