Difference between revisions of "1996 IMO Problems/Problem 5"
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Let <math>s_{1}=\left| AB \right|,\;s_{2}=\left| BC \right|,\;s_{3}=\left| CD \right|,\;s_{4}=\left| DE \right|,\;s_{5}=\left| EF \right|,\;s_{6}=\left| FA \right|</math> | Let <math>s_{1}=\left| AB \right|,\;s_{2}=\left| BC \right|,\;s_{3}=\left| CD \right|,\;s_{4}=\left| DE \right|,\;s_{5}=\left| EF \right|,\;s_{6}=\left| FA \right|</math> | ||
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+ | Let <math>d_{1}=\left| FB \right|,\;d_{2}=\left| BD \right|,\;d_{1}=\left| DF \right|</math> | ||
{{alternate solutions}} | {{alternate solutions}} |
Revision as of 13:30, 13 November 2023
Problem
Let be a convex hexagon such that
is parallel to
,
is parallel to
, and
is parallel to
. Let
,
,
denote the circumradii of triangles
,
,
, respectively, and let
denote the perimeter of the hexagon. Prove that
Solution
Let
Let
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.