How Does Time Dilation Affect Measurements of Earth's Size from Satellites?

[Zman]

The GPS satellites in stationary orbit around the Earth have clocks that run a little faster than the clocks on the surface of the earth. This is predicted in Einstein’s GTR.
Because of this the satellite clocks have to be synchronised on a regular basis with those on the earth.

Assuming that the speed of light is constant regardless of the strength of the gravitational field. Can I assume this?

And for the sake of argument let the satellite clock run 10% faster than the clocks on earth.
If the satellite measures the time taken for light to go between two points on the earth, it will measure the time as 10% bigger than Earth based observers.
Because distances are all effectively defined by the speed of light does the Earth then seem 10% bigger from the satellite?

 

[JesseM]

Assuming that the speed of light is constant regardless of the strength of the gravitational field. Can I assume this?

This is true in a local sense, so if you construct a coordinate system using freefalling rulers and clocks in a small region of spacetime where the curvature is negligible, the speed of light will be c as measured in this coordinate system. But over a larger region where the curvature of spacetime is significant, then depending on what coordinate system you use in this region (and in GR you can use basically any coordinate system you want), the coordinate speed of light may not be constant.