MathDB

IMO Shortlist 2011, G6

Source: IMO Shortlist 2011, G6

July 13, 2012

geometryincentersymmetryreflectionIMO Shortlist

Problem Statement

Let

ABC

be a triangle with

AB=AC

and let

D

be the midpoint of

AC

. The angle bisector of

\angle BAC

intersects the circle through

D,B

and

C

at the point

E

inside the triangle

ABC

. The line

BD

intersects the circle through

A,E

and

B

in two points

B

and

F

. The lines

AF

and

BE

meet at a point

I

, and the lines

CI

and

BD

meet at a point

K

. Show that

I

is the incentre of triangle

KAB

.
Proposed by Jan Vonk, Belgium and Hojoo Lee, South Korea

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