Question 8
A circle $X$ is inscribed in a quadrilateral $PQRS$. Construct 4 circles $A, B, C, D$, each of which is tangent to 3 of the 4 straight lines determined by the sides of the quadrilateral, as shown in the figure below. Suppose that the radii of the circles $A, B, C, X$ are $2$, $1$, $4$, $3$, respectively. Determine the radius of the circle $D$.
