C

Step 1: Identify the positions. The object is at the center of curvature (C) of the concave mirror, which we will take as the origin (0, 0). The plane mirror is placed at a distance of 10 cm from the object, which means its coordinate is (-10 cm, 0).
Step 2: Determine the image formation in the plane mirror. The image formed by the plane mirror will be at the same distance behind the mirror. Thus, the image coordinate from the plane mirror's perspective will be (-20 cm, 0).
Step 3: Now, this image acts as an object for the concave mirror, located at (-20 cm, 0). Since the concave mirror's focal length is half of the radius of curvature, for a mirror with a center of curvature (C) at (0, 0) and focal length = R/2, the object is located at -20 cm. Using the mirror formula: \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \), where \( u = -20 \text{ cm} \) (object distance), we find the image distance (v).
Step 4: Substitute f = -10 cm (since f = R/2 and R = 20 cm): \( \frac{1}{-10} = \frac{1}{-20} + \frac{1}{v} \)
\( \frac{1}{v} = \frac{1}{-10} + \frac{1}{20} = -\frac{1}{20} \)
Hence, \( v = -20 \text{ cm} \).
Step 5: Image coordinates from the concave mirror perspective are (0 + (-20 cm), 0), which gives us (-20 cm, 0). Thus, combining all the reflections, the final image coordinates are (-20 cm, 0).
Therefore, the coordinates of the image formed are (-20 cm, 0), which corresponds to option C.