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IMO Shortlist 2012, Geometry 3

Source: IMO Shortlist 2012, Geometry 3

July 29, 2013

geometrycircumcirclehomothetyIMO Shortlistradical axisSpiral Similarity

Problem Statement

In an acute triangle

ABC

the points

D,E

and

F

are the feet of the altitudes through

A,B

and

C

respectively. The incenters of the triangles

AEF

and

BDF

are

I_1

and

I_2

respectively; the circumcenters of the triangles

ACI_1

and

BCI_2

are

O_1

and

O_2

respectively. Prove that

I_1I_2

and

O_1O_2

are parallel.

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