1990 USAMO Problems/Problem 5

Revision as of 11:26, 11 February 2008 by 1=2 (talk | contribs) (Resources)

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

Resources

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