Difference between revisions of "1961 IMO Problems/Problem 5"

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==See Also==
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{{IMO box|year=1961|num-b=4|num-a=6}}
 
 
[[1961 IMO Problems]]
 

Revision as of 19:17, 25 October 2007

Problem

Construct a triangle ABC if the following elements are given: $AC = b, AB = c$, and $\angle AMB = \omega \left(\omega < 90^{\circ}\right)$ where M is the midpoint of BC. Prove that the construction has a solution if and only if

$b \tan{\frac{\omega}{2}} \le c < b$

In what case does equality hold?


Solution

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1961 IMO (Problems) • Resources
Preceded by
Problem 4
1 2 3 4 5 6 Followed by
Problem 6
All IMO Problems and Solutions