Problem
GEO-B2-M05-P023 Angle of Two Circles Through the Centre
#23
★★★★★ Level 5 of 5
Circles \(\omega_1\) and \(\omega_2\) pass through \(O\) and meet again at \(A\). Prove that the angle between their image lines equals the angle between the circles at \(A\).
Both circles map to lines, which meet at \(A'\).
Since both circles pass through \(O\), their images are lines. Point \(A\) maps to \(A'\), and both image lines pass through \(A'\). Inversion preserves the angle between curves at \(A\ne O\), so the angle between the image lines equals the original angle between the circles.
A good problem on turning an angle of circles into an angle of lines.