  For any integer $n\ge 2$, a square can be partitioned into $n^2$ smaller
squares via a checkerboard-type dissection. Does there such a class-preserving
grid dissection exist for some other types of quadrilaterals? For instance, is
it true that a tangential quadrilateral can be partitioned into $n^2$ smaller
tangential quadrilaterals using an $n\times n$ grid dissection? We prove that
the answer is affirmative for every integer $n\ge 2$.
