Placing random line segments within polygon?

I would like to generate multiple line segments of a fixed length, a random bearing, and both segment endpoints within the polygon. It's not clear from the example, but it's fine if the segments intersect each other or span the indented features as long as both endpoints are in the polygon.

I also want the attributes table to include lat/lon for each segment endpoint and the azimuth between the endpoints.

Is this possible?