6) Find the value of x.

In triangle AHB, angle AHB = 90 degrees. OA is the radius of the circle. AH = 5. OB is the radius of the circle. OH is perpendicular to AB. In right-angled triangle OHA, OA^2 = OH^2 + AH^2. In right-angled triangle OHB, OB^2 = OH^2 + HB^2. Since OA = OB (radii), OH^2 + AH^2 = OH^2 + HB^2, which implies AH = HB. Thus, H is the midpoint of AB. Triangle OAB is an isosceles triangle. OH is the altitude from O to AB, so OH is also the median and angle bisector. In right-angled triangle AHB, we have AH = 5. We are given that the angle OAB = x. In triangle OHA, angle OHA = 90 degrees. Angle OAH = x. Therefore, angle AOH = 90 - x. In triangle OHB, angle OHB = 90 degrees. Angle OBH = angle OAB = x (since triangle OAB is isosceles). Therefore, angle BOH = 90 - x. Angle AOB = angle AOH + angle BOH = (90 - x) + (90 - x) = 180 - 2x. In triangle OAB, OA = OB. Angle OAB = Angle OBA = x. The sum of angles in triangle OAB is 180 degrees. So, angle AOB + angle OAB + angle OBA = 180. Angle AOB + x + x = 180. Angle AOB = 180 - 2x. This is consistent. We are given AH = 5. In right triangle OHA, tan(x) = OH/AH. We don't know OH. We are given that the length of the segment AH is 5. In right triangle AHB, we have AH = 5. We are also given that angle OAB = x. In triangle OHA, angle OHA = 90 degrees. Angle OAH = x. Therefore, angle AOH = 90 - x. In triangle OHB, angle OHB = 90 degrees. Since OH is perpendicular to AB and OA = OB, triangle OAB is isosceles and OH bisects AB. So AH = HB = 5. In right triangle AHB, tan(angle OBA) = AH/HB = 5/5 = 1. So angle OBA = 45 degrees. Since triangle OAB is isosceles with OA=OB, angle OAB = angle OBA = 45 degrees. Therefore, x = 45 degrees. The diagram shows that the length of AH is 5. In right triangle OHA, angle OHA = 90 degrees. Angle OAH = x. Angle AOH = 90 - x. In right triangle OHB, angle OHB = 90 degrees. Angle OBH = angle OAB = x. Angle BOH = 90 - x. Since OH is perpendicular to AB, H is the midpoint of AB. So AH = HB = 5. In right triangle AHB, tan(angle OBA) = AH/HB = 5/5 = 1. Thus, angle OBA = 45 degrees. Since triangle OAB is isosceles with OA = OB, angle OAB = angle OBA = 45 degrees. Therefore, x = 45 degrees.