Source — Euclid's Elements, encoded as an rrxiv paper

; bisect them at

,

(I.10). Join

,

. In

and

:

given,

by construction,

common; by I.8 the triangles are congruent, so

, and by I.13 both are right. Similarly

. By III.3 (rewriting it as: the perpendicular at the midpoint of a chord passes through the centre), both

produced and

produced pass through the centre. Their intersection

is therefore the centre.