Difference between revisions of "1961 IMO Problems/Problem 4"
((Previous edit was to slightly reword problem) Added solution.)
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Revision as of 01:23, 8 February 2009
Since triangles and share the base , we have , where denotes the area of triangle . Similarly, . Adding all of these gives , or We see that we must have at least one of the three fractions less than or equal to , and at least one greater than . These correspond to ratios being less than or equal to , and greater than or equal to , respectively, so we are done.
|1961 IMO (Problems) • Resources|
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