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IMO Shortlist 2013, Geometry #4

Source: IMO Shortlist 2013, Geometry #4

July 10, 2014

geometrycircumcircleIMO Shortlistgeometry solvedIsosceles TriangleAngle ChasingInversion

Problem Statement

Let

ABC

be a triangle with

\angle B > \angle C

. Let

P

and

Q

be two different points on line

AC

such that

BQ

and

ABC

is located between

P

and

C

. Suppose that there exists an interior point

D

of segment

BQ

for which

PD=PB

. Let the ray

AD

intersect the circle

ABC

at

R \neq A

. Prove that

QB = QR

.

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