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Bosnia and Herzegovina JBMO TST 2017 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2017

September 16, 2018

geometryincircleright angleincenter

Problem Statement

Let

ABC

be a triangle such that

\angle ABC = 90 ^{\circ}

. Let

I

be an incenter of

ABC

and let

F

D

and

E

be points where incircle touches sides

AB

BC

and

AC

, respectively. If lines

CI

and

EF

intersect at point

M

and if

DM

and

AB

intersect in

N

, prove that

AI=ND