Previous analysis Euler's rotation theorem

figure 2: arcs connecting preimage α , image of bisector ao of angle @ a.

now on initial circle (the blue circle), image on transported circle (red). labels image point a. since on transported circle (red), image of point on initial circle (blue) , labels preimage α (see figure 2). considers 2 arcs joining α , a. these arcs have same length because arc αa mapped onto arc aa. also, since o fixed point, triangle αoa mapped onto triangle aoa, these triangles isosceles, , arc ao bisects angle ∠αaa.

figure 3: o goes o′, o′ must coincide o.