Astroid is Envelope of Line Segment whose End Points lie on Coordinate Axes

Theorem
Let $\LL$ be a line segment of length $a$.

Let the endpoints of $\LL$ be constrained to lie on the coordinate axes of a Cartesian plane: one on the $x$-axis and one on the $y$-axis

The envelope of $\LL$ forms an astroid whose cusps lie on the points at which the coordinate axes intersect a circle of radius $a$ whose center is at the origin.