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.

## Solution

The length x=2√(ab).

This solution uses Sawayama’s Lemma.

## Poem

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