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PQ is parallel to BC

Source: 2013 China TST Quiz 1 Day 1 P1

March 30, 2013

geometrycircumcirclegeometric transformationreflectiongeometry proposed

Problem Statement

The quadrilateral

ABCD

is inscribed in circle

\omega

.

F

is the intersection point of

AC

and

BD

.

BA

and

CD

meet at

E

. Let the projection of

EF

on

AB

and

CD

be

G

and

H

, respectively. Let

M

and

N

be the midpoints of

BC

and

EF

, respectively. If the circumcircle of

\triangle MNG

only meets segment

BF

at

P

, and the circumcircle of

\triangle MNH

only meets segment

CF

at

Q

, prove that

PQ

is parallel to

BC

.

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