Construction of inverse point in sphere

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i would like to know if my construction of inverse point of A in sphere, A' is right. First of all i constructed a line through pole $S$ and $A$, then i drew a line through $N$ perpendicular to $AS$. Their point of intersection i named $I$. Then, intersection of $NI$ and $OA$ is an image of $A$, $A'$. enter image description here