The three circles have different radii. Each pair of circles has two external tangents that intersect at a point. According to Monge's Theorem, the three intersections are collinear, as shown by the yellow line.
Drag the center of a circle to move it. Drag the circle itself to resize it. The three intersections always remain collinear. (The mobile version is under construction.)
If internal tangents are used instead of external tangents, the intersections are not necessarily collinear. What if internal tangents are used for just two of the circle pairs, leaving one pair with external tangents?
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