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