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ASU 408 All Soviet Union MO 1985 |A_2A_3| + |MN| = circumradius

Source:

August 5, 2019

geometryarccircumradiuscircumcircle

Problem Statement

The

[A_0A_5]

diameter divides a circumference with the

O

centre onto two hemicircumferences. One of them is divided onto five equal arcs

A_0A_1, A_1A_2, A_2A_3, A_3A_4, A_4A_5

. The

(A_1A_4)

line crosses

(OA_2)

and

(OA_3)

lines in

M

and

N

points. Prove that

(|A_2A_3| + |MN|)

equals to the circumference radius.