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
![](https://mirangu.com/wp-content/uploads/2022/02/WheelsInMotionSolution.jpg)
Visual solution
![](https://mirangu.com/wp-content/uploads/2022/02/WheelsInMotionSolutionDavid.jpg)
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
![](https://mirangu.com/wp-content/uploads/2022/02/WheelsInMotionBella.jpg)
One reply on “Wheels in motion”
In the Soiridonov diagram the triangle with the two red sides is a right triangle, so alpha+beta=90• so the angle at middle green dot, which is 2 alpha plus 2 beta, is 180•
Thus the problem still works when the lengths 1,2,sqrt(2) are replaced by any a,b,sqrt(ab).