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Concurrent lines(or parallel)

Source: RMM 2016 Day 1 Problem 1

February 27, 2016

geometryRMMRMM 2016

Problem Statement

Let

ABC

be a triangle and let

D

be a point on the segment

BC, D\neq B

and

D\neq C

. The circle

ABD

meets the segment

AC

again at an interior point

E

. The circle

ACD

meets the segment

AB

again at an interior point

F

. Let

A'

be the reflection of

A

in the line

BC

. The lines

A'C

and

DE

meet at

P

, and the lines

A'B

and

DF

meet at

Q

. Prove that the lines

AD, BP

and

CQ

are concurrent (or all parallel).

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