This question already has an answer here:
- Triangle with incircle [closed] 2 answers
Generalizing a puzzle from Mind Your Decisions, here's something that I found to be rather neat.
Suppose that AB$=c$, AC$=b$, and BC$=a$. What's the perimeter of $\triangle$CDE?
Clue: The coveted tick will go to the most attractive, visual proofs/arguments that don't use any additional variables! Judges decision etc.