Identical circles have their centers aligned as shown, with the middle circle inscribed in a triangle. Show that the outer circles can be made tangent to the green circumcircle if the red axis is rotated correctly.

Scroll down for a solution to this problem.

## Solution

If such a configuration is possible then it must conform to the diagram below which is compatible with the Euler formula for the distance between Incentre and Circumcentre.

## 3 replies on “Circle triplet”

I show the solution for an equilateral triangle.

Jpg

I was hoping that someone would prove this without resorting to Euler’s theorem that the square of the distance between the incenter and the circumcenter is R(R-2r). Then we would have had a “new” proof of that theorem.