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Pass through the same point but i think well known

Source: BMO 2006 problem 2

May 2, 2006

geometrycircumcircleprojective geometryalgebrapolynomialpower of a pointradical axis

Problem Statement

Let

ABC

be a triangle and

m

a line which intersects the sides

AB

and

AC

at interior points

D

and

F

, respectively, and intersects the line

BC

at a point

E

such that

C

lies between

B

and

B_1

. The parallel lines from the points

A

,

B

,

C

to the line

m

intersect the circumcircle of triangle

ABC

at the points

C

,

B_1

and

C_1

, respectively (apart from

A

,

B

,

C

). Prove that the lines

A_1E

,

B_1F

and

C_1D

pass through the same point. Greece

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