Since no respondents provided a solution to his last problem, Prof. Aliyev is willing to offer one more chance to unravel his mysterious diagrams. In the accompanying figure, nonintersecting circles with radii r < R have common external tangent lines A B and C D , where the named points are the points of tangency.…

As shown in Figure 4, A B C is a triangle. Points F and E lie on side A B , with F closer to B . Point D lies on side A C . Point G is the intersection of segments B D and C E , and H is the intersection of ray…

Call a function f mapping the real numbers to themselves a sign-flipping function if for all x , y ∈ R , ( x − y ) ( f ( x ) + f ( y ) ) = ( x + y ) f ( x − y ) . For example, the identity…