I am looking for the best strategy to find 2 circles whose total area are maximum in a triangle. I tried it on an example as seen Figures below.
If I draw a big circle that touchs to 3 sides and then to draw 3 circles next to the big circle. Then select the biggest one in three of them. As seen in Figure 1 that I found Max Area of 2 circles: 14.18+4.56=18.74
To drew 2 circles that each one touched to 2 sides of triangles and also touching each other as seen in Figure-2. I tried to extend total area that what I got in Strategy 1 but I could not.
Of course I know my example is not proof that Strategy 1 is general solution of the problem. I just tried to show what I did till now to solve the optimum problem.
Could you please help me to find the best strategy and to proof it for that optimum problem? Note:If there is a general strategy proof for total max area for n circles in a triangle, It can be wonderful. Thanks for your answers and your time.