MathDB

12

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

Several coins with collinear centers

Source: XVII Sharygin Correspondence Round, P12

3/2/2021
Suppose we have ten coins with radii 1,2,3,…,101, 2, 3, \ldots , 10 cm. We can put two of them on the table in such a way that they touch each other, after that we can add the coins in such a way that each new coin touches at least two of previous ones. The new coin cannot cover a previous one. Can we put several coins in such a way that the centers of some three coins are collinear?
geometry