**Discover and prove a theorem about two lines tangent to a circle at the endpoints of a diameter**

**Answer:**

The lines are parallel. There’s a theorem (I forget what it’s called) that says that a line that runs tangent to a circle is perpendicular to the radius at that point. Since the diameter might as well be the radius for these purposes (they’re 180\textdegree apart), two lines that make the same angle with the same line are parallel.