In the circle below, AB is parallel to CD, AD is a diameter of the circle, and AD = 36.What is the length of AB?
+128460 From the center of the circle (call it O ) connect OB
Then OB = OA = 18
So angle BAO =angle ABO = 42°
Then angle AOB = 180 - 2(42) = 180 - 84 = 96°
Using the Law of Cosines
AB^2 = (OA)^2 + (OB)^2 -2 (OA * OB) cos (AOB)
AB^2 = (18)^2 + (18)^2 - 2(18*18) cos (96)
AB = sqrt [ (18)^2 + (18)^2 - 2(18*18) cos (96) ]
AB = sqrt (715.7) ≈ 26.75
