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# Interior perpendicular bisector of a triangle

## Description

The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly bisects that side. The three perpendicular bisectors of a triangle’s three sides intersect at the circumcenter (the center of the circle through the three vertices). Thus any line through a triangle’s circumcenter and perpendicular to a side bisects that side. In an acute triangle the circumcenter divides the interior perpendicular bisectors of the two shortest sides in equal proportions. In an obtuse triangle the two shortest sides’ perpendicular bisectors (extended beyond their opposite triangle sides to the circumcenter) are divided by their respective intersecting triangle sides in equal proportions. For any triangle the interior perpendicular bisectors are related to the lengths of the sides of the triangle and its area.

Related formulas

## Variables

 pa The interior perpendicular bisector falling on side a (m) a Side of the triangle opposite to angle A (m) T The Area of the triangle (m2) b Side of the triangle opposite to angle B (m) c Side of the triangle opposite to angle C (m)