MathDB

Iberoamerican Olympiad 2008, problem 5

Source:

September 24, 2008

geometrygeometric transformationhomothetyratiocircumcircleanalytic geometryinequalities

Problem Statement

Let

ABC

a triangle and

X

,

Y

and

Z

points at the segments

BC

,

AC

and

AB

, respectively.Let

A'

,

B'

and

C'

the circuncenters of triangles

AZY

,

BXZ

,

CYX

, respectively.Prove that

4(A'B'C')\geq(ABC)

with equality if and only if

AA'

,

BB'

and

CC'

are concurrents. Note:

(XYZ)

denotes the area of

XYZ

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