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Germany: Three lines AA', BB' and CC' have a common point.

Source: German TST 4, P1, 2009, Exam set by Christian Reiher

July 18, 2009

geometrygeometry unsolved

Problem Statement

Let

I

be the incircle centre of triangle

ABC

and

\omega

be a circle within the same triangle with centre

I.

The perpendicular rays from

I

on the sides

\overline{BC}, \overline{CA}

and

\overline{AB}

meets

\omega

A', B'

and

C'.

Show that the three lines

AA', BB'

and

CC'

have a common point.