Let O1 be the circle inscribed in CAB angle of any triangle ABC (inside that

triangle). O2 is the circle, inscribed in ABC angle (inside triangle too)

and extangent to O1. O3, O4, O5, O6, O7 let us define in the same way.

Does anybody know the proof of O1=O7 (i.e. the chain of such circles

consists not more than of the six circles?)

Is that problem well-known?

Best regards,

Yours sincerely,

Alex