Editing Semiperimeter (section)

===Properties===

In any triangle, any vertex and the point where the opposite [[excircle]] touches the triangle partition the triangle's perimeter into two equal lengths, thus creating two paths each of which has a length equal to the semiperimeter. If {{mvar|A, B, B', C'}} are as shown in the figure, then the segments connecting a vertex with the opposite excircle tangency ({{mvar|{{overline|AA'}}, {{overline|BB'}}, {{overline|CC'}}}}, shown in red in the diagram) are known as [[Splitter (geometry)|splitters]], and

:<math>\begin{align}
s &= |AB|+|A'B|=|AB|+|AB'|=|AC|+|A'C| \\
  &= |AC|+|AC'|=|BC|+|B'C|=|BC|+|BC'|.
\end{align}</math>

The three splitters [[Concurrent lines|concur]] at the [[Nagel point]] of the triangle.

A [[Cleaver (geometry)|cleaver]] of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. So any cleaver, like any splitter, divides the triangle into two paths each of whose length equals the semiperimeter. The three cleavers concur at the [[Spieker center|center of the Spieker circle]], which is the [[incircle]] of the [[medial triangle]]; the Spieker center is the [[center of mass]] of all the points on the triangle's edges.

A line through the triangle's [[incenter]] [[Bisection|bisects]] the perimeter if and only if it also bisects the area.

A triangle's semiperimeter equals the perimeter of its [[medial triangle]].

By the [[triangle inequality]], the longest side length of a triangle is less than the semiperimeter.