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)
 13–16  4.0

Problem

The triangle \(C_1C_2O\) is given. Within it the bisector \(C_2C_3\) is drawn, then in the triangle \(C_2C_3O\) – bisector \(C_3C_4\) and so on. Prove that the sequence of angles \(\gamma_n = C_{n + 1}C_nO\) tends to a limit, and find this limit if \(C_1OC_2 = \alpha\).