Problem
GEO-B2-M05-P015 Two Circles Through the Centre
#15
★★★★☆ Level 4 of 5
Circles \(\omega_1\) and \(\omega_2\) pass through \(O\) and meet again at \(A\). Prove that their images are two lines meeting at \(A'\).
Each circle through \(O\) maps to a line.
Both circles pass through the centre of inversion, so both map to lines. Their common point \(A\) maps to \(A'\), so \(A'\) lies on both image lines. Therefore the lines meet at \(A'\).
A standard inversion picture with centre at a common point.