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Intermediate

Polarisation

Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.

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Solution

Solution by Zero Quantum ?=!.
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2 replies on “Polarisation”

Notice that the radius of the blue circle is s-a, the radius of the purple circle is s, and the radius of the circle inscribed in the little right triangle (whose sides are a,b,c) is s-c. There is also a 4th circle, not shown, whose radius is s-b.

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