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Internally tangent circles have their common tangent in between the circles. Externally tangent circles have their common tangents above and below the circles.

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Contest problems often need this idea together with one or two others. That is where understanding goes deeper than memory. These are real problems from the AMC 8, AMC 12 and AIME, the national math competitions for middle and high school students, each with a worked solution on LIVE by Po-Shen Loh.

Type a concept, like “slope” or “photosynthesis”.

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