Carnot's Theorem
Revision as of 10:21, 26 August 2008 by 1=2 (talk | contribs) (New page: '''Carnot's Theorem''' states that in a triangle <math>ABC</math> with <math>A_1\in BC</math>, <math>B_1\in AC</math>, and <math>C_1\in </math>AB<math>, perpendiculars to the sides...)
Carnot's Theorem states that in a triangle 
with 
, 
, and 
AB![$, [[perpendicular]]s to the sides$](http://latex.artofproblemsolving.com/4/8/1/481598de23f197434bc9aa5809642cc12f7802b7.png)
BC, 
, and 
at 
, 
, and 
are concurrent if and only if 
.
Contents
Proof
Problems
Olympiad
is a triangle. Take points 
on the perpendicular bisectors of 
respectively. Show that the lines through 
perpendicular to 
respectively are concurrent. (Source)
