3850.11 – Rhombi, Locus of Vertex

Let $AB$ and $AC$ be noncollinear rays issuing from the common endpoint $A$. Let rhombi be drawn, many rhombi, each having one vertex at $A$, one vertex on $AB$, and one vertex on $AC$. What is the locus of the fourth vertex?

Solution

The desired locus is the bisector of the angle at $A$ between the given rays.