## Heron triangles & half-angle formulae

Prove that

If the sides of a triangle are in arithmetic progression if and only if the cotangents of its half-angles

$\cot \, (A/2)$,    $\cot \, (B/2)$,    $\cot \, (C/2)$

are also in arithmetic progression

Also,   if and only if     $\tan \, (A/2) \, \tan \, (C/2) \; = \; 1/3$

The sequence of the squares of the side lengths is in arithmetic progression if and only if

$\cot \, A$,    $\cot \, B$,    $\cot \, C$   is also an arithmetic progression.