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concyclic Points

Source: 2014 Korea Junior Olympiad Round 2 #1

September 29, 2016

geometry

Problem Statement

Given

\triangle ABC

with incenter

I

. Line

AI

meets

BC

at

D

. The incenter of

\triangle ABD, \triangle ADC

are

E,F

, respectively. Line

DE

meets the circumcircle of

\triangle BCE

at

P(\neq E)

and line

DF

meets the circumcircle of

\triangle BCF

at

Q(\neq F)

. Show that the midpoint of

BC

lies on the circumcircle of

\triangle DPQ

.

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