The sacrosanct circles

Two tangent circles and two tangent line segments meeting in a point on the outer circle. The tangency points are connected by a line segment of length x. What’s x in terms of a and b?

Scroll down for a solution to this problem.


The length x=2√(ab).

Solution by Ignacio Larrosa Cañestro.

This solution uses Sawayama’s Lemma.


The sacrosanct circle
Is a virtuous circle
May be to share solidarity
A circle that we see positively
For the earth and for humanity
Sacrosanct circles that create
Knowledge and creation mutually
Hoping to engage happiness and quality
A virtuous circle of methodology


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