Problem
GEO-B2-M05-P013 Angle Preservation
#13
★★★☆☆ Level 3 of 5
Two circles meet at \(P\ne O\) at an angle of \(40^\circ\). Prove that their images meet at \(P'\) at an angle of \(40^\circ\).
Inversion preserves angles at points different from the centre.
Point \(P\) is not the centre of inversion, so the angle between the curves is preserved. Therefore the angle between the images at \(P'\) equals the original angle \(40^\circ\).
At this level, this is a fact to be applied.