Answer:
AB = 3.464.
Step-by-step explanation:
Here we are given that OA = AC = 2
Therefore, ΔOAC is an equilateral triangle and ∡OCA = 60°
Therefore, ∡ACB = 120° (sum of angles on a straight line)
Where ∡OAC + ∡CAB = 90° (Angle of a tangent) and ∡OAC = 60° (interior angle of an equilateral triangle) hence, ∡CAB = 30°
Therefore, since ∡OBC + ∡ACB + ∡CAB = 180°, we have;
∡OBC + 120° + 30° = 180°, hence ∡OBC = 30°
From trigonometric ratios, tan(∡OBC) = OA/AB
∴ tan(30°) = 2/AB which gives
AB = 2/(tan(30°) = 3.464
AB = 3.464.
