The second circle has the center C(100 , -10) and . The x-axis is tangent to this circle.
Make a rough sketch of the situation. (see attachment. My sketch is not drawn to scale because the distance between the centers of the circles is too large - and the greater circle belongs to the left side)
You have 2 unknowns: x and . Use the 2 right triangles to set up a system of equations:
You'll get two solutions:
1. A small circle with it's center at and
2. A huge circle which touches the 2 circles from below and the tangent point to the straight line is very far away at the right. (I'll only give you the approximate values):
M(603.4280150, -6033.780150) and r = 6034.780150