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 
.
