The steam locomotive

Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?

Scroll down for a solution to this problem.


The proportion a : b is √(R/(R+r)).

Solution by 諺風説子 using the Tangent-secant theorem.


The steam locomotive
A jewel of the railway birth
Rack and pinion locomotive
Pulled so many wagons
And made us people happy
Powerfull machine
Very popular at altitude
They accompanied our travels
Our dreams of escape
Our love stories and our tears
The steam loco so friendly


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