One of the Iranian scientists of the fourth and fifth centuries AH is Āzarkhor Asht\={a}z Goshnasp. His name is only mentioned in the works of the prominent Iranian scientist, Ab\={u} Rayh\={a}n al-B\={i}r\={u}n\={i}. In this paper, we will explain \={A}zarkhor's two proofs on the first theorem of the book ``al-Estekhr\={a}j al-Awt\={a}r" that given by Ab\={u} Rayh\={a}n. This theorem is called ``Theorem of the broken chord" and these two proofs are the only mathematical legacy left by \={A}zarkhor
