# Find the radius of three identical circles which touch each other externally.

Three identical circles touch each other externally. The tangents at their point of contact meet at a point whose distance from any point of contact is 2 cm. The radius of the circles is?

• Draw a diagram and find out at what angles the 3 common tangents meet. You will know what to do next.. – Qwerty Jun 25 '16 at 15:18
• Almost the same as this math.stackexchange.com/questions/1838093/… – almagest Jun 25 '16 at 18:17
• @almagest Seriously?? Almost same as that???? Nevertheless read what this kid has written below my answer...you will laugh. – User Not Found Jun 27 '16 at 13:37
• @ArghyaChakraborty I said almost because I knew no closer would accept it as a duplicate. – almagest Jun 27 '16 at 13:43
• That kind of thing no longer surprises me. This site has everyone from lazy kids age 8 who want their homework done up to Fields Medal winners! To be fair maths is a subject where things tend to be impossibly difficult until the moment when they switch to being tiresomely trivial! – almagest Jun 27 '16 at 13:57

Ok so $OE$ is 2cm and $AE$ is r. So, $AO=\sqrt{4+r^2}$. Similarly $CE=\sqrt{4+r^2}+2=\sqrt{3r^2}$. Solve it you get answer as $2\sqrt{3}$
• @Akshit $CE=CO+2$ and $CO=AO$ by congruence...and if you like my answer you can accept it by clicking on the tick mark left to my answer. If you have more doubts, feel free to ask. – User Not Found Jun 26 '16 at 14:50
• @Akshit You don't even need congruence...see $\angle ACO=\angle CAO$ which means $AO=CO$. The angles are equal as angles $A,B,C$ are all $60^\circ$ and also $AO,BO,CO$ all bissect the angles as the triangle is equilateral. – User Not Found Jun 27 '16 at 2:06