Difference between revisions of "1969 Canadian MO Problems/Problem 9"
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Revision as of 13:10, 28 July 2006
Problem
Show that for any quadrilateral inscribed in a circle of radius the length of the shortest side is less than or equal to .
Solution
Let be the sides and be the diagonals. By Ptolemy's theorem, . However, the diameter is the longest possible diagonal, so and .
If , then which is impossible. Proof by contradiction.