(adsbygoogle = window.adsbygoogle || []).push({}); 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 [Broken]

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Circle Geometry

**Physics Forums | Science Articles, Homework Help, Discussion**