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Median IPQ bisects arc BAC

Source: S.A booklet 2021 P8 in problems without solution

September 20, 2021

geometryIMOgeometry unsolved

Problem Statement

Let

ABC

be an non-isosceles triangle with incenter

I

, circumcenter

O

and a point

D

on segment

BC

such that

(BID)

cut segments

AB

at

E

and

(CID)

cuts segment

AC

at

F

Circle

(DEF)

cuts segments

AB

,

AC

again at

M,N

. Let

P

The intersection of

IB

and

IPQ

,

Q

The intersection of

IC

and

DF

. Prove that

EN,FM,PQ

are parallel and the median of vertex

I

in triangle

IPQ

bisects the arc

BAC

of

(O)

.

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