Carnot's Theorem
Given any triangle 
, the signed
sum of perpendicular distances from the circumcenter 
to the sides (i.e., signed lengths of the pedal
lines from 
) is
 |
where 
is the inradius
and 
is the circumradius.
The sign of the distance is chosen to be negative iff the entire segment 
lies outside
the triangle.
Explicitly,
 |
where 
is the area of triangle 
.
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triangle properties
