Circles with colinear (on X axis) centersWorking entirely in the quadrant where x and y are positive, I'm looking for a trig-based solution for something I can easily construct with a compass but can't (yet) find the elegant solution. Given a circle in normal orientation, then picking a point somewhere on that circle in that upper, right quadrant, I seek a way to locate the center of another circle that intersects that chosen point on the first circle, constrained by that second circle center staying on the x axis.
Noobs can't post pix, but it sure would be easier to describe using the labels in this linked pic: original circle of center C and radius CA; point B is target of intersectio by new circles with centers at F and G whose radii are FE and GD respectively; AD = AE & AD < AH (actually, not interested in AD approaching AH, which would push GD off toward infinity; similarly disinterested in angle ACB approaching extremes of zero or pi/2 rads)