# Find the radius of the circle?

Three circles of equal radii have been drawn inside an equilateral triangle , of side a , such that each circle touches the other two circles as well as two sides of triangle.

Then find the radius of the circle. I tried but could not get where to start. I think we need to relate the center of circle with either incentre / circumcenter.

Will there be any relation between incentre / circumcenter with the centres of 3 circles?

How i can achieve this? Thanks in advance.

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If you get something like $x+2\cdot(x\cdot\tan\frac{\pi}{6})+x=a$ then you are thinking in the right direction, I guess.
$$a=2r +2r\tan 60^{\circ} \Rightarrow a=2r(1+\sqrt 3) \Rightarrow r=\frac{a}{2(1+\sqrt 3)}$$