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.
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:
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??
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