Calculate distance between centroid and edge of polygon on given azimuth

I need to find the distance between the centroid and the edge of polygon on given azimuth.

One solution, that comes to my mind is to create a line starting on centroid and make it long enough to cross the edge (so for example make it a fixed 100km or come up with something more elaborate) and then split it by polygon.

That way, first segment gives me desired length.
However, this solution seems to be not very reliable and unnecessarily complex. Is there a simpler, better way to compute such distance?