1997 USAMO Problems/Problem 2
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Problem
is a triangle. Take points 
on the perpendicular bisectors of 
respectively. Show that the lines through 
perpendicular to 
respectively are concurrent.
Solution
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Let the perpendicular from A meet FE at A'. Define B' and C' similiarly. By Carnot's Thereom, The three lines are concurrent if
But this is clearly true, since D lies on the perpendicular bisector of BC, BD = DC.
QED
| 1997 USAMO (Problems) | ||
| Preceded by Problem 1 | 1 • 2 • 3 • 4 • 5 | Followed by Problem 3 |
| All USAMO Problems and Solutions | ||
