Carnot's Theorem
Carnot's Theorem states that in a triangle with
,
, and
, perpendiculars to the sides
AC
AB
A_1
B_1
C_1
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. Unknown error_msg)\triangle ABCD, E, F
BC, CA, AB
A, B, C
EF, FD, DE$ respectively are concurrent. (Source)