Apollonius Problems

Three unequal ponds are perfect circles.
Scouts want to camp at equal distance from the three ponds. Help them to choose the exact place.

Example :
The diameters of ponds are D1=60, D2=100, D3=80
The distances from edge to edge betweeen the ponds are d12=70, d13=70, d23=40
Distance from camp to pond edges ? solution

Geometric construction (with compass and straightedge) ?

Consider the cases when some ponds are wells (just points) or rivers (lines).
Some cases are obvious (3 wells for instance - solution)
How many different cases to consider ? solution

Details

 

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