1971 Canadian MO Problems
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Contents
Problem 1
is a chord of a circle such that
and
Let
be the center of the circle. Join
and extend
to cut the circle at
Given
find the radius of the circle
Problem 2
Let and
be positive real numbers such that
. Show that
.
Problem 3
is a quadrilateral with
. If
is greater than
, prove that
.
Problem 4
Determine all real numbers such that the two polynomials
and
have at least one root in common.