Prove that if the four points of intersection of the circles and by the lines and…

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Prove that if the four points of intersection of the circles

x^2 + y^2 + ax + by + c = 0

and

x^2 + y^2 + a'x + b'y + c' = 0

by the lines

Ax + By + C = 0

and

A'x + B'y + C' = 0

respectively are concyclic, then

\begin{vmatrix} a-a' & b-b' & c-c' \\ A & B & C \\ A' & B' & C' \end{vmatrix} = 0.