$PQRS$ is a rectangle with a centre $C$. $PQ$ has length $4$ and $PS$ has length 12. The circles meet $PS$ at $U$ and $V$ with both having radius $1$. $PU$ has length $1$ and $PV$ has length $4$. What is $PW$?
I’ve tried this problem for days and tried to find answers elsewhere but I can’t do it. Tried getting areas of triangles to find altitudes and was working with trapeziums and such. Made lots of approaches but I always get stuck.
Best Answer
Every straight line through $C$ divides the area of the rectangle in half, every line through the point $D$ in the middle between the centers of both circles does the same for the shaded area. Our line CW must do both, i.e. it passes through $D$. If we take $C$ as the origin of our coordinate system, $D$ has coordinates $(-7/2,-1)$, so the slope of $CW$ is $2/7$, and $\displaystyle PW=2-6\cdot\frac27=\frac27$.