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MathNet 2012 Question 90

Math Olympiad Vault · MathNet 2012

Question 90

Jüri wishes to draw $n$ circles and any number of lines on the plane such that all the lines meet at one point, and for every two circles there exist two lines that touch both of these circles.

a)
Is it possible for Jüri to solve this problem for any $n \ge 2$?

b)
For which natural numbers $n$ is it possible to solve this problem if in addition all the circles must have the same radius?