Problem #PRU-73828

Problems Methods Examples and counterexamples. Constructive proofs Pigeonhole principle Pigeonhole principle (other) Set theory and logic Theory of algotithms Theory of algorithms (other)

Problem

The triangle C1C2O is given. Within it the bisector C2C3 is drawn, then in the triangle C2C3O – bisector C3C4 and so on. Prove that the sequence of angles γn=Cn+1CnO tends to a limit, and find this limit if C1OC2=α.