### Thinking about Geometry

Can you find a right-angled triangle for which the inscribed circle has a radius of $6$?
In the solution we substituted the specific case of $r=6$ into our equations at a fairly early stage.
However, we might have asked ourselves, why $r=6$? What about other values of $r$? Presumably we can take the same approach for any radius but if we have to return to the early stages of working for each specific case that we want to consider then we aren’t being very efficient.