Construction algorithm

In our previous post, we have learnt about Similar Triangles and the Right Triangle Altitude Theorem. Today, continuing our journey in the garden of geometry, we want to find answer to the following question

Given a line segment of length $r$, by compass and straightedge, what kind of shapes can we construct? 

How to construct a regular polygon with 15 sides

To feed your curiosity, today we will look at a compass and straightedge construction of the regular polygon with 15 sides and we will show that there is a connection between this construction problem with the measuring liquid puzzle that we have learned from our previous post.