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incircle of triangle

Source: All-Russian 2007

May 4, 2007

geometrycircumcirclegeometry proposed

Problem Statement

The incircle of triangle

ABC

touches its sides

BC

,

AC

,

AB

at the points

A_{1}

,

B_{1}

,

C_{1}

respectively. A segment

AA_{1}

intersects the incircle at the point

Q\ne A_{1}

. A line

\ell

through

A

is parallel to

BC

. Lines

A_{1}C_{1}

and

A_{1}B_{1}

intersect

\ell

at the points

P

and

R

respectively. Prove that

\angle PQR=\angle B_{1}QC_{1}

. A. Polyansky

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