**Solution to Monge's Theorem Problem 5**

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Two circles are ALWAYS a dilation of each other. This is due to the fact that all circles are similar and relate in size by a ratio of their radii. The dilation of two circles is NOT unique. There are a whole line of centers of dilations collinear with the centers of the circles that would yield the dilation if given the right scale factor. As seen in Part II, the tangents to the circle also intersect on the line collinear with the circle centers.

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