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?

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    $\begingroup$ Draw a diagram and find out at what angles the 3 common tangents meet. You will know what to do next.. $\endgroup$ – Qwerty Jun 25 '16 at 15:18
  • $\begingroup$ Almost the same as this math.stackexchange.com/questions/1838093/… $\endgroup$ – almagest Jun 25 '16 at 18:17
  • $\begingroup$ @almagest Seriously?? Almost same as that???? Nevertheless read what this kid has written below my answer...you will laugh. $\endgroup$ – User Not Found Jun 27 '16 at 13:37
  • $\begingroup$ @ArghyaChakraborty I said almost because I knew no closer would accept it as a duplicate. $\endgroup$ – almagest Jun 27 '16 at 13:43
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    $\begingroup$ 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! $\endgroup$ – almagest Jun 27 '16 at 13:57

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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 $2\sqrt{3}$

  • $\begingroup$ How is CE=AO+2 ? $\endgroup$ – Akshit Jun 26 '16 at 6:09
  • $\begingroup$ @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. $\endgroup$ – User Not Found Jun 26 '16 at 14:50
  • $\begingroup$ i can't understand how the triangles are congruent? I am probably missing some basic stuff thats not striking. $\endgroup$ – Akshit Jun 26 '16 at 15:20
  • $\begingroup$ @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. $\endgroup$ – User Not Found Jun 27 '16 at 2:06
  • $\begingroup$ There is no proof that the angles bisect each other. How are you coming to that? $\endgroup$ – Akshit Jun 27 '16 at 11:35

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