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The context is construction of three circles with different radii so that they touch each other externally using a graduated ruler and a compass.

I have done it by drawing a triangle where each side is the sum of the radii of distinct combination of two circles and then drawing the circles by taking the vertex as the centre of a circle.

My question is why does my method work and is this the standard method to do the construction in context because i could not find anything about it on the internet.

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Your method works well. If you draw the line segments between each pair of centers they are composed of two radii, which justifies your construction.

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    Is this the standard method? – 2017-02-11
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    I would say so, but don't really know as I don't teach the subject. It is simple and easy to justify, so it should be. – 2017-02-11