I came across the following problem in my self-study of real analysis:
For any real numbers $a$ and $b$, show that $\max \{a,b \} = \frac{1}{2}(a+b+|a-b|)$ and $\min\{a,b \} = \frac{1}{2}(a+b-|a-b|)$
So $a \geq b$ iff $a-b \ge0$ and $b \ge a$ iff $b-a \ge 0$. At first glance, it seems like an average of distances. For the first case, go to the point $a+b$, add $|a-b|$ and divide by $2$. Similarly with the second case.
Would you just break it up in cases and verify the formulas? Or do you actually need to come up with the formulas?