Answer
Convex; -38.0 cm.
Work Step by Step
Use the mirror equation, 23–2.
$$\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}$$
Here, the object is at $d_o=\infty$.
$$\frac{1}{\infty}+\frac{1}{d_i}=\frac{1}{f}$$
Solve for the focal length. The image distance is a negative number, because the image is behind the mirror.
$$f=d_i=-19.0cm$$
The radius is twice the focal length, or $r = -38.0cm$.
The focal length is negative, so the mirror is convex, aka a diverging mirror.
