1972 Canadian MO

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\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 $a_1, a_2, ... , a_n$ be non-negative numbers. Define $M$ to be the sum of all of products of pairs $a_ia_j$