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Regional Olympiad - FBH 2015 Grade 10 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

September 23, 2018

geometryincentercircumcircle

Problem Statement

Let

ABC

be a triangle with incenter

I

. Line

AI

intersects circumcircle of

ABC

in points

A

and

D

(A \neq D)

. Incircle of

ABC

touches side

BC

in point

E

. Line

DE

intersects circumcircle of

ABC

in points

D

and

F

(D \neq F)

. Prove that

\angle AFI = 90^{\circ}