# Three Circles and Collinear Centers of Dilation

DevFeed: [Three Circles and Collinear Centers of Dilation](<https://devfeed.tech/articles/three-circles-and-collinear-centers-of-dilation-40225.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/07/13/three-circles-and-collinear-centers-of-dilation/>)

Published: 2011-07-13T16:29:14Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [mathematics](<https://devfeed.tech/tags/mathematics.md>)

## AI overview

A geometric proof shows that the centers of dilation for each pair of three non-intersecting circles with distinct radii are collinear. The proof lifts the circles into three-dimensional cones and uses intersecting planes to establish collinearity.

## Source excerpt

Problem: Suppose their are three circles in the plane of distinct radii. For any two of these circles, we may find their center of dilation as the intersection point of their common tangents. For example, in the following picture we mark the three centers of dilation for each pair of circles: We notice that the three centers of dilation are collinear. Show they are always collinear for any three non-intersecting circles of distinct radii.