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Iran Geometry

Source: Iran MO 3rd round 2017 finals - Geometry P3

September 3, 2017

geometrycircumcircle

Problem Statement

In triangle

ABC

points

P

and

Q

lies on the external bisector of

\angle A

such that

B

and

P

lies on the same side of

AC

. Perpendicular from

P

to

AB

and

QC

to

AC

intersect at

X

. Points

P'

and

Q'

lies on

PB

and

QC

such that

PX=P'X

and

QX=Q'X

. Point

T

is the midpoint of arc

BC

(does not contain

A

) of the circumcircle of

ABC

. Prove that

P',Q'

and

T

are collinear if and only if

\angle PBA+\angle QCA=90^{\circ}

.

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