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Iran Geometry

Source: Iran MO 3rd round 2017 finals - Geometry P2

September 3, 2017

geometrycircumcircle

Problem Statement

Assume that

P

be an arbitrary point inside of triangle

ABC

.

BP

and

CP

intersects

AC

and

AB

in

E

and

F

, respectively.

EF

intersects the circumcircle of

ABC

in

B'

and

C'

(Point

E

is between of

F

and

B'

). Suppose that

B'P

and

C'P

intersects

BC

in

C''

and

B''

respectively. Prove that

B'B''

and

C'C''

intersect each other on the circumcircle of

ABC

.

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