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Problem 5 -- Making A Point Here

Source: 46th Austrian Mathematical Olympiad National Competition Part 2 Problem 5

July 14, 2018

geometryincenterAustriaAUT

Problem Statement

Let I be the incenter of triangle

ABC

and let

k

be a circle through the points

A

and

B

. The circle intersects
* the line

AI

in points

BC

and

P

* the line

BI

in points

B

and

Q

* the line

AC

in points

A

and

R

* the line

BC

in points

B

and

S

with none of the points

A,B,P,Q,R

and

S

coinciding and such that

R

and

S

are interior points of the line segments

AC

and

BC

, respectively.
Prove that the lines

PS

,

QR

, and

CI

meet in a single point.
(Stephan Wagner)

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