This past week, one of my students stopped me on my first pass around the class with the exciting words "I think I discovered a theorem! In a right triangle, the angles the median makes with the hypotenuse are twice the other angles!" We had discussed the median to the hypotenuse in the previous class, but I'd never thought about the angles before. So I started doing algebra in my head, confirming the relationship he was describing:

Before I could get very far, Vik showed me the elegant diagram below:

With the inscribed angle theorem, the proof is immediate.

Eureka!