The eighth proposition in the third book of the Elements is one of Euclid's most complex propositions. It shows that a segment through an outside point and a circle is shortest when it lies
on the line passing through the center , as illustrated above. Euclid also describes the near and
far halves of the circumference.
According to Billingsley (1570), the proposition "is called commonly, in old books amongst the barbarous, the Peacock Tail."
and a circle is shortest when it lies
on the line passing through the center 
, as illustrated above. Euclid also describes the near and
far halves of the circumference.
