Projecting Azimuthal Equidistant global map into circle using QGIS

How do I change the projection of a map in QGIS?

First, click on Settings > Project properties. Then, click on the box labelled as Enable on the fly CRS transformation. Next, select the projection which the current layer and all the subsequent layers will be using in common.
 

How is an azimuthal map projection made?

The azimuthal projection plots the surface of Earth using a flat plane. Imagine light rays radiating from a source following straight lines. Those light rays intercept the globe onto a plane at various angles. The light source can be emitted from different positions developing different azimuthal map projections.
 

Can a map be azimuthal and equidistant?

Azimuthal equidistant projection maps can be useful in terrestrial point to point communication. This type of projection allows the operator to easily determine in which direction to point their directional antenna.