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altitudes and incenters lead to perpendicularity

Source: Cono Sur Shortlist 2009 G4

July 26, 2019

geometryperpendicularaltitudesincenter

Problem Statement

Let

AA _1

and

CC_1

be altitudes of an acute triangle

ABC

. Let

I

and

J

be the incenters of the triangles

AA_1C

and

AC_1C

respectively. The

C_1J

and

A_1 I

lines cut into

T

. Prove that lines

AT

and

TC

are perpendicular.

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