Two tangent circles and a third circle touching the line segment connecting their centres in the tangency point. Prove that the red points (centre and two intersection points) are collinear.

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## Solution

## Visual solution

## Poem

Wheels in motion

Could be bicycles or car wheels

But also starting an action

Opening new perspectives and negociations

And set agreements to get the wheels in motion

I need courage

Vision and passion

To get the wheels of change in motion in time

Through this life of mine

## One reply on “Wheels in motion”

In the Soiridonov diagram the triangle with the two red sides is a right triangle, so alpha+beta=90â€¢ so the angle at middle green dot, which is 2 alpha plus 2 beta, is 180â€¢

Thus the problem still works when the lengths 1,2,sqrt(2) are replaced by any a,b,sqrt(ab).