2. In the diagram, TU and TV are tangents to
   a circle, centre .
   Given that OTU , calculate
   

To tackle the scenario where TU and TV are tangents to a circle with center O, let’s dive into some fun facts. When two tangents are drawn from a point outside the circle, they hold special properties. For instance, the angles formed between the tangent lines and the radius to the point of tangency are always complementary to one another, making it easier to calculate the required angles using the tangential angle theorem.

Now, for a real-world application, consider the use of tangents and circles in designing roundabouts. Traffic engineers utilize these geometric principles to ensure smooth vehicle movement while maintaining safe distances. Understanding the angles and tangents helps in modeling the ideal dimensions and layouts for efficient traffic flow. So, the next time you’re zooming around a roundabout, remember that splendid geometry is at play!