while reading The Art of Problem Solving: Volume 1, I came across this proof in chapter 19 that a reflection of a circle is a congruent circle:
"Let the original oenter be $O$, the radius of the circle be $r$, and the reflection of $O$ be $O'$. If the point $P$ is on the original circle, then $OP=r$. The image of $OP$ is $O'P'$, where $P'$ is the image of $P$, so $O'P'=r$ because lengths are preserved. Thus the image of $P$ is on a circle of radius $r$.
Are we done? No. For all we know at this point, the image of a circle could be a semicircle."
I'm a little confused, how could reflecting a circle produce a semicircle ? I thought reflections preserve shape and distance ?