Problem #PRU-73828

Problems Methods Examples and counterexamples. Constructive proofs Pigeonhole principle Pigeonhole principle (other) Discrete Mathematics Algorithm Theory Theory of algorithms (other)

13–16 4.0

Problem

The triangle $C_{1} C_{2} O$ is given. Within it the bisector $C_{2} C_{3}$ is drawn, then in the triangle $C_{2} C_{3} O$ – bisector $C_{3} C_{4}$ and so on. Prove that the sequence of angles $γ_{n} = C_{n + 1} C_{n} O$ tends to a limit, and find this limit if $C_{1} O C_{2} = α$ .

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