A New Proof of the Centre Circle Chain

DeLongchamps⁽¹⁾ (1877), and Pesc⁽²⁾(1891) proved by elementary methods⁽³⁾ the following chain of theorems:

Theorem. Given n lines in a plane, the centre-circles of sets of (n-I) of these will be concurrent, also the centres of these will lie on a circle-the centre-circle of the n lines. The centre-circle of thret lines is the circumcircle of the triangle formed by them.