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It is given that the image formed by the convex mirror should be at radius of curvature . Why it should?
I guess that the question is based on the experiment to determine the focal length of a convex mirror using convex lens.
Initially a convex lens is used to obtain a real image of a candle. (or pin if you are doing the experiment using the optical bench) Then a convex mirror is kept in such a way that the image is obtained on the same position as the object. This happens when the rays are incident normal to the mirror. The rays of light incident normal to the mirror are directed towards the centre of curvature. Since the image was formed by the rays which are now reflected normally, the distance between the convex mirror and the original position of image gives the radius of curvature.
See the diagram for illustration.