If it is to create the sphere, a boss per revolution of a line is a semicircle, so the center of the sphere will be the midpoint of the line,
If the sphere exists, a 3d sketch of a right triangle whose vertices are tengeant to the sphere, so the center will be the midpoint of the hypotenuse. It also seems to me that a constraint of concentrecity with a point is also feasible!
If the sphere was created with SolidWorks, it was probably based on a sketch with an arc of a circle whose center is the center of the sphere. Just make the sketch visible to access this point later.
If the sphere has been imported and does not have a sketch for its generation: simply measure the diameter of the sphere, then build a 3D sketch with a simple segment and a point in the middle. The ends of this segment are constrained to be on the spherical surface, and the distance from the midpoint to one end of the segment is dimensioned with the value of the radius. The segment in question is then a diameter of the sphere, its midpoint being the center.
@fauteux1959: Unfortunately, I don't have a version of SolidWorks compatible with the 2015...
The principle of the last @Lynk proposal seems to me to be the most effective: to construct two segments carried by two spokes. The center is at the intersection of these segments. The attached video offers a simplified version of this principle, which avoids the construction of the two tangent planes.
I put a short film where I present the way to create a shot with three references, I managed to create the first two references, the center of the two spheres. But the third I don't know what to put the final plane would be inclined through the center of two spheres
Here is another solution to recover the center of a spherical, or partially spherical, element. The advantage of this solution is that it does not use tangency (in a sketch or between faces) which tend to be capricious.
-1 copy the spherical surface with " Surface-Offset "
-2 Transform the copied surface which is a portion of a sphere into a complete sphere with " Surface restore "
-3 Create a " Point " (Reference Geometry -> Point) with the option "Center of the surface".
Well yes! It's logical you wrote center of the surface which excludes the tail of the sphere. Morality do not confuse surface and body, which is what I did when I asked you the question. I cover my head with ashes and I have a pledge it's noted ;-)