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Bosnia and Herzegovina JBMO TST 2012 Problem 1

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2012

September 16, 2018

circlepentagongeometry

Problem Statement

On circle

k

there are clockwise points

A

B

C

D

and

E

such that

\angle ABE = \angle BEC = \angle ECD = 45^{\circ}

. Prove that

AB^2 + CE^2 = BE^2 + CD^2