26 TK = x

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle. The arc KT subtends angle KOT at the center and angle SKT at the circumference. Angle KOT = 2 * angle SKT. Since SK is a chord and angle SKT = 60 degrees, the arc KT subtends 60 degrees at K. The angle subtended by arc KT at the center O is angle KOT. Angle KOT = 2 * 60 = 120 degrees. Triangle KOT is an isosceles triangle with OK = OT (radii). The sum of angles in triangle KOT is 180 degrees. Angle OKT = Angle OTK = (180 - 120) / 2 = 30 degrees. The radius is given as 10. Using the Law of Sines in triangle KOT: KT / sin(120) = OK / sin(30). KT = OK * sin(120) / sin(30) = 10 * (sqrt(3)/2) / (1/2) = 10 * sqrt(3). Therefore, x = 10 * sqrt(3).