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circumradius, incenter, ...

Source: IMO Shortlist 2007, G7

July 6, 2008

geometrycircumcircleincenterreflectionIMO Shortlist

Problem Statement

Given an acute triangle

ABC

with

\angle B > \angle C

. Point

I

is the incenter, and

R

the circumradius. Point

D

is the foot of the altitude from vertex

A

. Point

K

lies on line

AD

such that AK \equal{} 2R, and

D

separates

A

and

K

. Lines

DI

and

KI

meet sides

AC

and

BC

at

E,F

respectively. Let IE \equal{} IF. Prove that

\angle B\leq 3\angle C

. Author: Davoud Vakili, Iran

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