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Regional Olympiad - FBH 2011 Grade 10 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

September 26, 2018

geometrycircumcircle

Problem Statement

Let

I

be the incircle and

O

a circumcenter of triangle

ABC

such that

\angle ACB=30^{\circ}

. On sides

AC

and

BC

there are points

E

and

D

, respectively, such that

EA=AB=BD

. Prove that

DE=IO

and

DE \perp IO