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Source: Romania JBMO TST 2024 Day 4 P2

July 31, 2024

geometryROMANIA JBMO TST

Problem Statement

Let

ABC

be a scalene triangle, with circumcircle

\omega

and incentre

I.{}

The tangent line at

C

to

\omega

intersects the line

AB

at

D.{}

The angle bisector of

BDC

meets

BI

at

P{}

and

AI{}

at

Q{}.

Let

M{}

be the midpoint of the segment

PQ.

Prove that the line

IM

passes through the middle of the arc

ACB

of

\omega.

Dana Heuberger

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