Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.
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Solution
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Polarisation
Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.
Scroll down for a solution to this problem.
Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear. https://t.co/qyArQY3UsN pic.twitter.com/YYm5ughBV4
— Mirangu (@Mirangu1) October 11, 2022
2 replies on “Polarisation”
Here are more details leading to a possible solution.
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.