1. The problem statement, all variables and given/known data There is a semicircle with radius 1. Two circles are inscribe in it with centres C1 and C2 and radius r1 and r2 respectively. Find the maximum possible value of r1+r2 Here is the picture, I have drawn. http://img143.imageshack.us/img143/8392/circlesdn3.png 3. The attempt at a solution I have constructed the tangents as shown in the figure. I have shown the right angles. And I also deduce that: AF=DF=CF From this I see that r1 is necessarily equal to r2. Isnt it?? But I am not sure if I have drawn DF right. It might not be a tangent to both circles in some cases?? Help me!