1972 Canadian MO
\textbf{1972 Canadian MO Problems and Solutions}
Problem 1:
Given three distinct unit circles, each of which is tangent to the other two, find the radii of the circles which are tangent to all three circles.
Solution:
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Problem 2:
Let be non-negative numbers. Define to be the sum of all of products of pairs , i.e.
Prove that the sqaure of at least one of the numbers a_1, a_2, ... a_n does not exceet .