Question

please explain the reason why the light rays passing through centre of curvature come back along the same path after reflection

Answer 1

A ray of light passing through the centre of curvature of a concave mirrorretraces its path (gets reflected along the same path), because as the ray of light passes through centre of curvature of a concave mirror it strikes the mirror along the normal i.e. it incidences on to the mirror at 90 degree.
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Answer 2

The center of curvature acts as a normal and as we know any ray passing through the normal comes back along the same path.
HENCE the rays passing through the center of curvature will come back along the same path.

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