title: Carnot's theorem (conics)
text: # Carnot's theorem (conics)
  
  Carnot's theorem (named after Lazare Carnot) describes a relation between conic sections and triangles.
  
  In a triangle $ABC$ with points $C_{A},C_{B}$ on the side $AB$, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle A_B, A_C} on the side $BC$ and $B_{C},B_{A}$ on the side $AC$ those six points are located on a common conic section if and only if the following equation holds:
  
      ${\frac {|AC_{A}|}{|BC_{A}|}}\cdot {\frac {|AC_{B}|}{|BC_{B}|}}\cdot {\frac {|BA_{B}|}{|CA_{B}|}}\cdot {\frac {|BA_{C}|}{|CA_{C}|}}\cdot {\frac {|CB_{C}|}{|AB_{C}|}}\cdot {\frac {|CB_{A}|}{|AB_{A}|}}=1$.
  