ShmoopTube

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Here’s your shmoop du jour, brought to you by interlocking circles.

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How many tangent lines can be drawn to exactly two circles in the picture below?

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Here are the potential answers...

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First up, let’s make sure we all know what a tangent is.

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And no, it's not a funky kind of orange.

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The one that connects at an arc or circle at exactly one point is a tangent.

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The easiest way to solve this problem is to start by imagining that one of these circles isn’t even there.

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Poof, it’s gone.

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There are all sorts of tangent lines we can draw to one of these circles…

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…but only two will hit both circles at exactly one point.

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Now if we do the same with a different pair of circles, we get the same result.

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Same deal with the final pair.

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So…looks like we get 2 tangents times 3 possible pairings…

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…for a grand total of 6 tangent lines.

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And boom, we’ve got our answer – option D.

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