Problem
GEO-B2-M05-P014 Tangency Is Preserved
#14
★★★☆☆ Level 3 of 5
Circles \(\omega_1\) and \(\omega_2\) are tangent at \(T\ne O\). Prove that their images are also tangent at \(T'\).
Tangency is an angle of \(0^\circ\).
At \(T\), the angle between the circles is \(0^\circ\). Inversion preserves angles at points different from the centre, so the angle between the images at \(T'\) is also \(0^\circ\). Hence the images are tangent.
A foundation for tangency problems.