Why is Descartes' theorem failing here?
I was doing a simple question :
Three circles of equal radii, equal to $1$ unit are touching each other. Find the radius of circle circumscribing the three circles.
My answer: Radius of circumcircle of triangle formed by joining the centre of the three smaller circles is $$2(√3/2)(2/3) = 2/√3$$
so, radius of circle circumscribing the three circle will be $$(2/√3) + 1$$ which is correct as per the book.
Then I thought of applying Descartes' theorem, which gave me $$1/(3+2√3)$$ which is wrong.
Am I committing any mistake? Why not both the answers are same? Please help.