1. The problem statement, all variables and given/known data There are two circles of equal radii. I have to prove that the mid point of the line joining their centres is the only point through which if several arbitrary lines are drawn, equal areas enclosed by the circles will fall on either side of the line. I cannot think of a way to proceed. I have observed the situation by drawing out equal cirlces and testing the conditions. They seem as obvious as the result of 2+2, but equally difficult to prove. Please help .