Problem
GEO-B2-M05-P009 Circle into a Line
#9
★★★☆☆ Level 3 of 5
A circle \(\omega\) passes through \(O\). Points \(A,B,C\ne O\) lie on \(\omega\). Prove that \(A',B',C'\) are collinear.
A circle through the centre of inversion maps to a line.
Since \(\omega\) passes through \(O\), its image is a line not passing through \(O\). All points \(A',B',C'\) lie on this image, hence they are collinear.
A basic transition from cyclicity to collinearity.