We are given a circle
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
with center
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
and radius
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
and a square
![Q](/media/m/4/5/c/45ce8d14aa1eb54f755fd8e332280abd.png)
with center
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
and side
![2](/media/m/e/e/e/eeef773d19a3b3f7bdf4c64f501e0291.png)
. Let
![XY](/media/m/1/c/e/1ce2b6bc5783d5ee7b3276a845f41d6e.png)
be the hypotenuse of an isosceles right triangle
![XY Z](/media/m/3/e/f/3efbad6de2f98acd58e0b0d5ab202d67.png)
. Describe the locus of points
![Z](/media/m/7/9/4/794ff2bd637e30ea27e50e57eecd0b76.png)
as
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
varies along
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
and
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
varies along the boundary of
%V0
We are given a circle $K$ with center $S$ and radius $1$ and a square $Q$ with center $M$ and side $2$. Let $XY$ be the hypotenuse of an isosceles right triangle $XY Z$. Describe the locus of points $Z$ as $X$ varies along $K$ and $Y$ varies along the boundary of $Q.$