Difference between revisions of "1990 USAMO Problems/Problem 5"

(Resources)
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== Resources ==
 
== Resources ==
  
* [[1990 USAMO Problems]]
+
{{USAMO box|year=1990|num-b=4|after=Final Question}}
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=356630#356630 Discussion on AoPS/MathLinks]
 
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=356630#356630 Discussion on AoPS/MathLinks]
  
 
[[Category:Olympiad Geometry Problems]]
 
[[Category:Olympiad Geometry Problems]]

Revision as of 11:26, 11 February 2008

Problem

An acute-angled triangle $ABC$ is given in the plane. The circle with diameter $\, AB \,$ intersects altitude $\, CC' \,$ and its extension at points $\, M \,$ and $\, N \,$, and the circle with diameter $\, AC \,$ intersects altitude $\, BB' \,$ and its extensions at $\, P \,$ and $\, Q \,$. Prove that the points $\, M, N, P, Q \,$ lie on a common circle.

Solution

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Resources

1990 USAMO (ProblemsResources)
Preceded by
Problem 4
Followed by
Final Question
1 2 3 4 5
All USAMO Problems and Solutions