Programming Interview Question : Prove that a circle will be surrounded by exactly (and maximum) 6 congruent circles if each circle makes contact with this central circle and no circles overlap

I have known since a child that a tennis ball is surrounded by exactly 6 tennis balls. Here I show a glass being surrounded by exactly 6 glasses :

HINT1 : Use the nature of Equilateral triangles.


HINT2 : By Nature I mean angle :)




Solution : 
This image is pretty self explanatory (though not pretty ...... I a paper cup!)

And so if the centers of each surrounding circle are separated by 60 degrees the full 360 is completed by (360/60) = 6 circles.

Enjoy!