Carnot's Theorem

Revision as of 08:03, 27 August 2008 by 1=2 (talk | contribs)

Carnot's Theorem states that in a triangle $ABC$ with $A_1\in BC$, $B_1\in AC$, and $C_1\in AB$, perpendiculars to the sides $BC,$AC$, and$AB$at$A_1$,$B_1$, and$C_1$are [[concurrent]] [[if and only if]]$A_1B^2+C_1A^2+B_1C^2=A_1C^2+C_1B^2+B_1A^2$.

==Proof== {{incomplete|proof}}

==Problems== ===Olympiad===$ (Error compiling LaTeX. ! Missing $ inserted.)\triangle ABC$is a triangle. Take points$D, E, F$on the perpendicular bisectors of$BC, CA, AB$respectively. Show that the lines through$A, B, C$perpendicular to$EF, FD, DE$ respectively are concurrent. (Source)

See also

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