Puzzle of the Week #107 - Pipework Problems

This is a real life problem I encountered in my job. To try to make explain it I’ll talk in terms of x,y,z coordinates.

There is one pipe heading from the negative–x direction towards the (0,0,0) origin point. 100mm before it reaches the origin, the pipe bends such that the radius of the centre line of the pipe is 100mm. After 90 degrees it straightens out so that it is heading on the +y axis.

A second pipe is heading from the +x direction towards the origin. Again it bends with a centre line radius of 100mm for 90 degrees before heading on the +z axis.

What is the minimum distance between the pipes' centre lines? I’ll be happy with 1 decimal place.